1049:
of the top-performing investment, and indeed will always be lower than the highest return (unless all returns are identical). Conversely, the diversified portfolio's return will always be higher than that of the worst-performing investment. So by diversifying, one loses the chance of having invested solely in the single asset that comes out best, but one also avoids having invested solely in the asset that comes out worst. That is the role of diversification: it narrows the range of possible outcomes. Diversification need not either help or hurt expected returns, unless the alternative non-diversified portfolio has a higher expected return.
1088:"Risk parity" is an alternative idea. This weights assets in inverse proportion to risk, so the portfolio has equal risk in all asset classes. This is justified both on theoretical grounds, and with the pragmatic argument that future risk is much easier to forecast than either future market price or future economic footprint. "Correlation parity" is an extension of risk parity, and is the solution whereby each asset in a portfolio has an equal correlation with the portfolio, and is therefore the "most diversified portfolio". Risk parity is the special case of correlation parity when all pair-wise correlations are equal.
5259:. While diversification in the modern sense was "not easily available in Keynes's day" and Keynes typically held a small number of assets compared to later investment theories, he nonetheless is recognized as a pioneer of financial diversification. Keynes came to recognize the importance, "if possible", he wrote, of holding assets with "opposed risks since they are likely to move in opposite directions when there are general fluctuations" Keynes was a pioneer of "international diversification" due to substantial holdings in non-U.K. stocks, up to 75%, and avoiding
51:
5159:
misses the point, because for an investor concerned with the value of his portfolio at the end of a period of time, it is the total return that matters, not the annualized return. Because of the effects of compounding, the standard deviation of the total return actually increases with time horizon. Thus, if we use the traditional measure of uncertainty as the standard deviation of return over the time period in question, uncertainty increases with time.
923:
5272:
911:
4022:
4927:. If one buys a single stock in the S&P 500, one is exposed both to index movements and movements in the stock based on its underlying company. The first risk is called "non-diversifiable", because it exists however many S&P 500 stocks are bought. The second risk is called "diversifiable", because it can be reduced by diversifying among stocks.
3668:
5153:
The argument is often made that time reduces variance in a portfolio: a "time diversification". A common belief is younger investors should avoid bonds and emphasize stocks, due to the belief investors will have time to recover from any downturns. Yet this belief has flaws, as John
Norstad explains:
1084:
Diversification has no maximum so long as more assets are available. Every equally weighted, uncorrelated asset added to a portfolio can add to that portfolio's measured diversification. When assets are not uniformly uncorrelated, a weighting approach that puts assets in proportion to their relative
5140:
In corporate portfolio models, diversification is thought of as being vertical or horizontal. Horizontal diversification is thought of as expanding a product line or acquiring related companies. Vertical diversification is synonymous with integrating the supply chain or amalgamating distributions
1048:
on a diversified portfolio will be identical to that on an undiversified portfolio. Some assets will do better than others; but since one does not know in advance which assets will perform better, this fact cannot be exploited in advance. The return on a diversified portfolio can never exceed that
5144:
Non-incremental diversification is a strategy followed by conglomerates, where the individual business lines have little to do with one another, yet the company is attaining diversification from exogenous risk factors to stabilize and provide opportunity for active management of diverse resources.
1020:
In finance, an example of an undiversified portfolio is to hold only one stock. This is risky; it is not unusual for a single stock to go down 50% in one year. It is less common for a portfolio of 20 stocks to go down that much, especially if they are selected at random. If the stocks are selected
1057:
There is no magic number of stocks that is diversified versus not. Sometimes quoted is 30, although it can be as low as 10, provided they are carefully chosen. This is based on a result from John Evans and
Stephen Archer. Similarly, a 1985 book reported that most value from diversification comes
5158:
This kind of statement makes the implicit assumption that given enough time good returns will cancel out any possible bad returns. While the basic argument that the standard deviations of the annualized returns decrease as the time horizon increases is true, it is also misleading, and it fatally
4937:
The capital asset pricing model argues that investors should only be compensated for non-diversifiable risk. Other financial models allow for multiple sources of non-diversifiable risk, but also insist that diversifiable risk should not carry any extra expected return. Still other models do not
5206:). This strategy of splitting wealth equally among available options is now known as "naive diversification", "Talmudic diversification" or "1/n diversification", a concept which has earned renewed attention since the year 2000 due to research showing it may offer advantages in some scenarios.
3660:
2552:
rather than decreasing. Thus, for example, when an insurance company adds more and more uncorrelated policies to its portfolio, this expansion does not itself represent diversification—the diversification occurs in the spreading of the insurance company's risks over a large number of
1108:
on the portfolio. Diversification can lower the variance of a portfolio's return below what it would be if the entire portfolio were invested in the asset with the lowest variance of return, even if the assets' returns are uncorrelated. For example, let asset X have stochastic return
4547:
4201:
4017:{\displaystyle \sigma _{P}^{2}=\sum _{i=1}^{n}x_{i}^{2}\underbrace {\mathbb {E} \left\right]^{2}} _{\equiv \sigma _{i}^{2}}+\sum _{i=1}^{n}\sum _{j=1,i\neq j}^{n}x_{i}x_{j}\underbrace {\mathbb {E} \left)(R_{j}-\mathbb {E} )\right]} _{\equiv \sigma _{ij}}}
4804:
4954:
worked out an empirical example of the gains from diversification. Their approach was to consider a population of 3,290 securities available for possible inclusion in a portfolio, and to consider the average risk over all possible randomly chosen
1017:". Dropping the basket will break all the eggs. Placing each egg in a different basket is more diversified. There is more risk of losing one egg, but less risk of losing all of them. On the other hand, having a lot of baskets may increase costs.
2542:
2211:
uncorrelated volatile assets to a portfolio, thereby increasing the portfolio's size, is not diversification, which involves subdividing the portfolio among many smaller investments. In the case of adding investments, the portfolio's return is
2838:
1464:
4886:
3375:
3367:
4903:
introduced the concepts of diversifiable and non-diversifiable risk. Synonyms for diversifiable risk are idiosyncratic risk, unsystematic risk, and security-specific risk. Synonyms for non-diversifiable risk are
4405:
3172:
3038:
2655:
4030:
4397:
2388:
1717:
1021:
from a variety of industries, company sizes and asset types it is even less likely to experience a 50% drop since it will mitigate any trends in that industry, company class, or asset type.
5844:
Prince C Nwakanma1, Monday
Aberiate Gbanador. Talmud and Markowitz Diversification Strategies: Evidence from the Nigerian Stock Market. Accounting and Finance Research Vol. 3, No. 2; 2014
5373:
2142:
4686:
2269:
4589:
5899:
Chambers, David and Dimson, Elroy, John
Maynard Keynes, Investment Innovator (June 30, 2013). Journal of Economic Perspectives, 2013, Vol 27, No 3, pages 1–18, Available at SSRN:
5202:. The formula given there is to split one's assets into thirds: one third in business (buying and selling things), one third kept liquid (e.g. gold coins), and one third in land (
4694:
1566:
2182:
5374:"see M. Nicolas J. Firzli, "Asia-Pacific Funds as Diversification Tools for Institutional Investors", Revue Analyse Financière/The French Society of Financial Analysts (SFAF)"
4236:
1928:
1833:
1801:
1211:
1179:
4891:
Thus, in an equally weighted portfolio, the portfolio variance tends to the average of covariances between securities as the number of securities becomes arbitrarily large.
4619:
4286:
2879:
2393:
2083:
1301:
4645:
5407:
2716:
2685:
1878:
In general, the presence of more assets in a portfolio leads to greater diversification benefits, as can be seen by considering portfolio variance as a function of
1956:
1769:
1743:
1257:
974:
is the process of allocating capital in a way that reduces the exposure to any one particular asset or risk. A common path towards diversification is to reduce
4326:
4306:
4256:
2705:
2202:
1896:
1873:
1853:
1626:
1606:
1586:
1484:
1341:
1321:
1231:
1147:
1127:
1346:
4815:
4931:
3655:{\displaystyle \sigma _{P}^{2}=\mathbb {E} \left)^{2}+\sum _{i=1}^{n}\sum _{j=1,i\neq j}^{n}x_{i}x_{j}(R_{i}-\mathbb {E} )(R_{j}-\mathbb {E} )\right]}
3180:
841:
5380:
5608:
5433:
5984:
870:
831:
796:
5915:
M. Lawlor (2016). The
Economics of Keynes in Historical Context: An Intellectual History of the General Theory, Palgrave Macmillan UK,
4542:{\displaystyle \sigma _{P}^{2}={\frac {1}{n^{2}}}\ {n}{\bar {\sigma }}_{i}^{2}+n(n-1){\frac {1}{n}}{\frac {1}{n}}{\bar {\sigma }}_{ij}}
1024:
Since the mid-1970s, it has also been argued that geographic diversification would generate superior risk-adjusted returns for large
953:
4196:{\displaystyle \sigma _{P}^{2}=\sum _{i=1}^{n}x_{i}^{2}\sigma _{i}^{2}+\sum _{i=1}^{n}\sum _{j=1,i\neq j}^{n}x_{i}x_{j}\sigma _{ij}}
6015:
3049:
2887:
2567:
609:
5671:
6462:
5639:
5553:
5408:"see Michael Prahl, "Asian Private Equity – Will it Deliver on its Promise?", INSEAD Global Private Equity Initiative (GPEI)"
4334:
5789:
2274:
622:
781:
17:
5940:
5920:
5773:
5478:
5354:
1631:
4934:
to the point that the portfolio's performance will suffer because the fees outweigh the gains from diversification.
1898:, the number of assets. For example, if all assets' returns are mutually uncorrelated and have identical variances
1061:
Given the advantages of diversification, many experts recommend maximum diversification, also known as "buying the
6678:
5338:
503:
6330:
6609:
6412:
2088:
263:
173:
4650:
2215:
4799:{\displaystyle \sigma _{P}^{2}={\frac {1}{n}}{\bar {\sigma }}_{i}^{2}+{\frac {n-1}{n}}{\bar {\sigma }}_{ij}.}
946:
915:
159:
5959:(2015), Jeffrey R. Brown and Caroline M. Hoxby, editors (p. 127–150). Conference held September 27–28, 2012.
5263:
at a time when university endowments in the U.S. and U.K. were invested almost entirely in domestic assets.
6008:
5252:
4555:
2561:
The expected return on a portfolio is a weighted average of the expected returns on each individual asset:
998:
variance of its constituent assets, and often less volatility than the least volatile of its constituents.
6295:
6187:
4900:
1066:
1489:
6359:
5537:
2147:
725:
439:
129:
1875:
were negatively correlated but diminished (though not eliminated) if they were positively correlated.
6028:
5988:
5538:
Using
Derivatives and Leverage To Improve Portfolio Performance, Institutional Investor, May 13, 2010
4209:
2537:{\displaystyle {\text{var}}=\sigma _{x}^{2}+\sigma _{x}^{2}+\dots +\sigma _{x}^{2}=n\sigma _{x}^{2},}
1901:
1806:
1774:
1184:
1152:
1028:
by reducing overall portfolio risk while capturing some of the higher rates of return offered by the
786:
671:
449:
223:
5570:
5449:
5163:
Three notable contributions to the literature on the fallacy of time diversification have been from
6305:
6270:
5430:
939:
475:
5255:
from the 1920s to his 1946 death with a stock-selection strategy similar to what was later called
4594:
4261:
2846:
1961:
1058:
from the first 15 or 20 different stocks in a portfolio. More stocks give lower price volatility.
6614:
6335:
6320:
6275:
6262:
6001:
5314:
5260:
5237:
1835:). Note that the favorable effect of diversification on portfolio variance would be enhanced if
118:
108:
6310:
5993:
5604:
5470:
1262:
1025:
277:
188:
5815:
2833:{\displaystyle \underbrace {{\text{Var}}(R_{P})} _{\equiv \sigma _{P}^{2}}=\mathbb {E} ]^{2}.}
6652:
6554:
6527:
6512:
6280:
6135:
6056:
5304:
5294:
5289:
5284:
4624:
1065:". Identifying that portfolio is not straightforward. The earliest definition comes from the
617:
228:
4974:=1,000, and even four stocks provide most of the reduction in risk compared with one stock.
2556:
1001:
Diversification is one of two general techniques for reducing investment risk. The other is
6657:
6589:
6579:
6534:
6467:
6300:
6051:
5765:
5758:
5299:
2663:
979:
813:
730:
434:
359:
293:
245:
88:
8:
6647:
6604:
6115:
5979:
5656:
5654:
E. J. Elton and M. J. Gruber, "Risk
Reduction and Portfolio Size: An Analytic Solution,"
5587:
5248:
1933:
1748:
1722:
1236:
991:
890:
880:
600:
557:
509:
454:
268:
5276:
5232:
Modern understanding of diversification dates back to the influential work of economist
4959:-asset portfolios with equal amounts held in each included asset, for various values of
1233:
of a one-unit (e.g. one-million-dollar) portfolio is placed in asset X and the fraction
6624:
6619:
6599:
6487:
6290:
6248:
6145:
6071:
5882:
5515:
5463:
5342:
5309:
5211:
4311:
4291:
4241:
2690:
2187:
1881:
1858:
1838:
1611:
1591:
1571:
1469:
1326:
1306:
1216:
1132:
1112:
903:
885:
735:
690:
639:
480:
369:
103:
6502:
6492:
6482:
6437:
6432:
6386:
6382:
6355:
6285:
6202:
6076:
6066:
5975:
5936:
5932:
5916:
5769:
5635:
5474:
5350:
4924:
1459:{\displaystyle {\text{var}}(qx+(1-q)y)=q^{2}\sigma _{x}^{2}+(1-q)^{2}\sigma _{y}^{2}}
791:
667:
562:
429:
424:
419:
393:
354:
178:
78:
5675:
5628:
6539:
6457:
6407:
6390:
6315:
6179:
6164:
5874:
5827:
5724:
5507:
4951:
1062:
1029:
863:
656:
630:
548:
541:
524:
470:
444:
331:
313:
298:
218:
209:
113:
98:
60:
34:
5550:
4941:
4881:{\displaystyle \lim _{n\rightarrow \infty }\sigma _{P}^{2}={\bar {\sigma }}_{ij}.}
6574:
6549:
6507:
6497:
6472:
6452:
6442:
6155:
6119:
6061:
5557:
5437:
5319:
5256:
5241:
5233:
4905:
1930:, portfolio variance is minimized by holding all assets in the equal proportions
1045:
1002:
846:
771:
762:
720:
685:
677:
485:
374:
288:
69:
5971:
5793:
50:
6522:
6378:
6374:
6365:
6233:
6212:
6160:
6150:
6140:
6130:
6099:
6081:
6024:
5533:
5164:
4930:
In the presence of per-asset investment fees, there is also the possibility of
4909:
1105:
1097:
1041:
975:
753:
591:
283:
253:
168:
135:
5831:
4986:
Ratio of
Portfolio Standard Deviation to Standard Deviation of a Single Stock
6672:
6629:
6517:
6427:
6417:
6370:
6350:
6243:
6192:
5551:
Parity
Strategies and Maximum Diversification, Putnam Investments, June, 2013
3362:{\displaystyle \sigma _{P}^{2}=\mathbb {E} \left)(R_{j}-\mathbb {E} )\right]}
995:
820:
776:
552:
514:
494:
379:
340:
93:
5728:
5696:
Samuelson, Paul (1963). "Risk and
Uncertainty: A Fallacy of Large Numbers".
1719:, which is less than what it would be at either of the undiversified values
6584:
6569:
6345:
6207:
6168:
5184:
2390:
and the variance of the portfolio return if the assets are uncorrelated is
1628:
in the expression for the variance of portfolio return gives the latter as
927:
745:
715:
575:
273:
150:
123:
5904:
6634:
6594:
6340:
6325:
6238:
6125:
6103:
6091:
6043:
5623:
5203:
4913:
2557:
Diversification with correlated returns via an equally weighted portfolio
335:
200:
145:
140:
83:
6217:
6197:
6111:
6107:
5952:
5886:
5519:
5495:
4920:
1078:
983:
570:
409:
345:
5957:
How the Financial Crisis and Great Recession Affected Higher Education
5742:
Kritzman, Mark (October 2005). "A New Twist on Time Diversification".
5349:. Upper Saddle River, New Jersey: Pearson Prentice Hall. p. 273.
6564:
5715:
Bodie, Zvi (May–June 1995). "On the Risk of Stocks in the Long Run".
5168:
875:
836:
519:
308:
303:
5900:
5878:
5816:"Markowitz Versus the Talmudic Portfolio Diversification Strategies"
5511:
1013:
The simplest example of diversification is provided by the proverb "
990:. If asset prices do not change in perfect synchrony, a diversified
6422:
5271:
4947:
2687:
is the proportion of the investor's total invested wealth in asset
1101:
323:
183:
5764:. Wheaton, Illinois: Tyndale House Publishers, Inc. 1996. p.
6477:
5460:
1044:
of the returns on all assets in the portfolio are identical, the
967:
42:
6023:
5854:
The Only Guide to a Winning Investment Strategy You'll Ever Need
6544:
5199:
4942:
An empirical example relating diversification to risk reduction
910:
195:
5605:"Adding risks: Samuelson's fallacy of large numbers revisited"
5180:
4809:
As the number of assets grows we get the asymptotic formula:
3167:{\displaystyle \sigma _{P}^{2}=\mathbb {E} \left)\right]^{2}}
3033:{\displaystyle \sigma _{P}^{2}=\mathbb {E} \left\right]^{2}.}
2650:{\displaystyle \mathbb {E} =\sum _{i=1}^{n}x_{i}\mathbb {E} }
1074:
1069:
which argues the maximum diversification comes from buying a
987:
414:
364:
6559:
5440:. II. Portfolios of Assets. Retrieved on November 20, 2008.
4894:
740:
707:
318:
258:
1035:
651:
4688:
is the average of the variances. Simplifying, we obtain
1091:
1085:
correlation can maximize the available diversification.
5247:
An earlier precedent for diversification was economist
5135:
4963:. Their results are summarized in the following table.
5337:
4983:
Average Standard Deviation of Annual Portfolio Returns
4392:{\displaystyle x_{i}=x_{j}={\frac {1}{n}},\forall i,j}
1771:(which respectively give portfolio return variance of
1343:
are uncorrelated, the variance of portfolio return is
4818:
4697:
4653:
4627:
4597:
4558:
4408:
4337:
4314:
4294:
4264:
4244:
4212:
4033:
3671:
3378:
3183:
3052:
2890:
2849:
2719:
2693:
2666:
2570:
2396:
2383:{\displaystyle (1/n)x_{1}+(1/n)x_{2}+...+(1/n)x_{n},}
2277:
2218:
2190:
2150:
2091:
1964:
1936:
1904:
1884:
1861:
1841:
1809:
1777:
1751:
1725:
1634:
1614:
1594:
1574:
1492:
1472:
1349:
1329:
1309:
1265:
1239:
1219:
1187:
1155:
1135:
1115:
5760:
Life Application Study Bible: New Living Translation
5622:
1259:is placed in Y, the stochastic portfolio return is
5865:Markowitz, Harry M. (1952). "Portfolio Selection".
4923:one is obviously exposed only to movements in that
5757:
5627:
5588:"Risk and uncertainty: A fallacy of large numbers"
5500:The Journal of Financial and Quantitative Analysis
5462:
5148:
4880:
4798:
4680:
4639:
4613:
4583:
4541:
4391:
4320:
4300:
4280:
4250:
4230:
4195:
4016:
3654:
3361:
3166:
3032:
2873:
2832:
2710:The variance of the portfolio return is given by:
2699:
2679:
2649:
2536:
2382:
2263:
2196:
2176:
2136:
2077:
1950:
1922:
1890:
1867:
1847:
1827:
1795:
1763:
1737:
1711:
1620:
1600:
1580:
1560:
1478:
1458:
1335:
1315:
1295:
1251:
1225:
1205:
1173:
1141:
1121:
5951:David Chambers, Elroy Dimson, Justin Foo (2015).
6670:
4820:
5935:(2007). 100 Minds That Made the Market. Wiley,
5496:"How Many Stocks Make a Diversified Portfolio?"
5194:for you do not know what risks might lie ahead.
2207:The latter analysis can be adapted to show why
1712:{\displaystyle \sigma _{x}^{2}\sigma _{y}^{2}/}
5953:Keynes, King's, and Endowment Asset Management
5609:Journal of Financial and Quantitative Analysis
5575:Journal of Financial and Quantitative Analysis
5461:James Lorie; Peter Dodd; Mary Kimpton (1985).
5209:Diversification is mentioned in Shakespeare's
5191:But divide your investments among many places,
1958:. Then the portfolio return's variance equals
6009:
5187:which was written in approximately 935 B.C.:
947:
5669:
1052:
5228:Therefore, my merchandise makes me not sad.
832:International Financial Reporting Standards
797:Separation of investment and retail banking
6016:
6002:
5813:
5219:My ventures are not in one bottom trusted,
954:
940:
5864:
5695:
5571:"General Proof that Diversification Pays"
5469:(2nd ed.). Dow Jones-Irwin. p.
5198:Diversification is also mentioned in the
3961:
3921:
3895:
3755:
3731:
3624:
3584:
3460:
3398:
3331:
3291:
3203:
3130:
3072:
2996:
2910:
2851:
2797:
2776:
2627:
2572:
2137:{\displaystyle n(1/n^{2})\sigma _{x}^{2}}
5741:
5270:
5222:Nor to one place; nor is my whole estate
4895:Diversifiable and non-diversifiable risk
4681:{\displaystyle {\bar {\sigma }}_{i}^{2}}
2264:{\displaystyle x_{1}+x_{2}+\dots +x_{n}}
5493:
5465:The Stock Market: Theories and Evidence
5450:Investment Guide Beginners Introduction
4399:. The portfolio variance then becomes:
2184:, which is monotonically decreasing in
14:
6671:
5905:http://dx.doi.org/10.2139/ssrn.2287262
5225:Upon the fortune of this present year:
1036:Return expectations while diversifying
5997:
5714:
4584:{\displaystyle {\bar {\sigma }}_{ij}}
1092:Effect of diversification on variance
1015:Don't put all your eggs in one basket
5985:An Introduction to Investment Theory
5431:An Introduction to Investment Theory
5179:Diversification is mentioned in the
5136:Corporate diversification strategies
1466:. The variance-minimizing value of
5820:The Journal of Portfolio Management
5236:in the 1950s, whose work pioneered
1149:, with respective return variances
1129:and asset Y have stochastic return
24:
4919:If one buys all the stocks in the
4830:
4591:is the average of the covariances
4377:
4331:In an equally weighted portfolio,
1561:{\displaystyle q=\sigma _{y}^{2}/}
871:Private equity and venture capital
782:Bank for International Settlements
25:
6690:
5965:
5901:https://ssrn.com/abstract=2287262
4288:is the covariance between assets
2177:{\displaystyle \sigma _{x}^{2}/n}
994:will have less variance than the
916:Business and Economics portal
6291:Conditional Value-at-Risk (CVaR)
5814:Duchin, Ran; Levy, Haim (2009).
5626:; Merton H. Miller (June 1972).
2843:Inserting in the expression for
921:
909:
504:Base erosion and profit shifting
49:
5945:
5926:
5909:
5893:
5858:
5847:
5838:
5807:
5782:
5750:
5735:
5708:
5689:
5663:
5648:
5634:. Holt Rinehart & Winston.
5615:
5597:
5580:
5563:
5347:Economics: Principles in Action
5251:, who managed the endowment of
5149:Fallacy of time diversification
4231:{\displaystyle \sigma _{i}^{2}}
1923:{\displaystyle \sigma _{x}^{2}}
1828:{\displaystyle \sigma _{y}^{2}}
1796:{\displaystyle \sigma _{x}^{2}}
1206:{\displaystyle \sigma _{y}^{2}}
1174:{\displaystyle \sigma _{x}^{2}}
6610:Strategic financial management
6413:Asset and liability management
5987:, Prof. William N. Goetzmann,
5660:50 (October 1977), pp. 415–437
5543:
5526:
5487:
5454:
5443:
5423:
5397:
5363:
5331:
4860:
4827:
4778:
4733:
4661:
4566:
4524:
4494:
4482:
4459:
3981:
3978:
3965:
3944:
3941:
3938:
3925:
3904:
3772:
3759:
3644:
3641:
3628:
3607:
3604:
3601:
3588:
3567:
3481:
3477:
3464:
3443:
3351:
3348:
3335:
3314:
3311:
3308:
3295:
3274:
3150:
3147:
3134:
3113:
3013:
3000:
2868:
2855:
2818:
2814:
2801:
2780:
2742:
2729:
2644:
2631:
2589:
2576:
2447:
2402:
2364:
2350:
2322:
2308:
2292:
2278:
2116:
2095:
2072:
2059:
2045:
2017:
2003:
1987:
1973:
1970:
1706:
1670:
1555:
1519:
1432:
1419:
1385:
1379:
1367:
1355:
1287:
1275:
1077:. This is the idea underlying
264:Collateralised debt obligation
174:Bull (stock market speculator)
13:
1:
5540:. Retrieved on June 21, 2010.
5325:
4980:Number of Stocks in Portfolio
610:Final consumption expenditure
5612:34, September 1999, 323-339.
5277:Asset Allocation on Wikibook
4614:{\displaystyle \sigma _{ij}}
4281:{\displaystyle \sigma _{ij}}
2874:{\displaystyle \mathbb {E} }
2553:part-owners of the company.
2078:{\displaystyle {\text{var}}}
1568:, which is strictly between
7:
6188:Operational risk management
5670:John Norstad (2012-12-22).
5266:
4901:capital asset pricing model
1067:capital asset pricing model
1032:of Asia and Latin America.
1008:
10:
6695:
6360:Proportional hazards model
6311:Interest rate immunization
5717:Financial Analysts Journal
5174:
842:Professional certification
440:Enterprise risk management
224:Offshore financial centres
6643:
6400:
6261:
6226:
6178:
6090:
6042:
6035:
6029:financial risk management
5989:Yale School of Management
5972:Macro-Investment Analysis
5832:10.3905/JPM.2009.35.2.071
5253:King's College, Cambridge
4996:
4993:
4238:is the variance on asset
1296:{\displaystyle qx+(1-q)y}
1053:Amount of diversification
787:Financial Stability Board
6306:First-hitting-time model
6271:Arbitrage pricing theory
4990:
4938:accept this contention.
476:Mergers and acquisitions
27:Risk reduction technique
6679:Financial risk modeling
6615:Stress test (financial)
6321:Modern portfolio theory
5790:"Ecclesiastes 11:2 NLT"
5729:10.2469/faj.v51.n3.1901
5315:Modern portfolio theory
5238:modern portfolio theory
4640:{\displaystyle i\neq j}
1608:. Using this value of
1073:share of all available
1026:institutional investors
5536:and Michael Mendelson
5494:Statman, Meir (1987).
5429:Goetzmann, William N.
5280:
5161:
4882:
4800:
4682:
4641:
4615:
4585:
4543:
4393:
4322:
4302:
4282:
4252:
4232:
4197:
4159:
4126:
4072:
4018:
3869:
3836:
3710:
3656:
3546:
3513:
3427:
3363:
3253:
3232:
3168:
3102:
3034:
2984:
2940:
2875:
2834:
2701:
2681:
2651:
2615:
2538:
2384:
2265:
2198:
2178:
2138:
2079:
1952:
1924:
1892:
1869:
1849:
1829:
1797:
1765:
1739:
1713:
1622:
1602:
1582:
1562:
1480:
1460:
1337:
1317:
1297:
1253:
1227:
1207:
1175:
1143:
1123:
1096:One simple measure of
278:certificate of deposit
6653:Investment management
6555:Investment management
6281:Replicating portfolio
6057:Sovereign credit risk
5630:The Theory of Finance
5305:Financial correlation
5295:Dollar cost averaging
5290:Coherent risk measure
5285:Central limit theorem
5274:
5171:, and Mark Kritzman.
5156:
4883:
4801:
4683:
4642:
4616:
4586:
4544:
4394:
4323:
4303:
4283:
4253:
4233:
4198:
4127:
4106:
4052:
4019:
3837:
3816:
3690:
3657:
3514:
3493:
3407:
3364:
3233:
3212:
3169:
3082:
3035:
2964:
2920:
2876:
2835:
2702:
2682:
2680:{\displaystyle x_{i}}
2652:
2595:
2539:
2385:
2266:
2199:
2179:
2139:
2080:
1953:
1925:
1893:
1870:
1850:
1830:
1798:
1766:
1740:
1714:
1623:
1603:
1583:
1563:
1481:
1461:
1338:
1318:
1298:
1254:
1228:
1208:
1176:
1144:
1124:
229:Conduit and sink OFCs
6658:Mathematical finance
6590:Risk-return spectrum
6580:Mathematical finance
6535:Fundamental analysis
6468:Exchange traded fund
6052:Consumer credit risk
5577:2, March 1967, 1-13.
5300:Equity repositioning
4816:
4695:
4651:
4625:
4595:
4556:
4406:
4335:
4312:
4292:
4262:
4242:
4210:
4031:
3669:
3376:
3181:
3050:
2888:
2847:
2717:
2691:
2664:
2568:
2394:
2275:
2216:
2188:
2148:
2089:
1962:
1934:
1902:
1882:
1859:
1839:
1807:
1775:
1749:
1723:
1632:
1612:
1592:
1572:
1490:
1470:
1347:
1327:
1307:
1263:
1237:
1217:
1185:
1153:
1133:
1113:
455:Financial statements
435:Credit rating agency
360:Repurchase agreement
6648:Financial economics
6605:Statistical finance
6371:Value-at-Risk (VaR)
6276:Black–Scholes model
6116:Holding period risk
5980:Stanford University
5657:Journal of Business
5343:Sheffrin, Steven M.
5249:John Maynard Keynes
4849:
4749:
4712:
4677:
4475:
4423:
4227:
4102:
4087:
4048:
3810:
3725:
3686:
3442:
3393:
3198:
3067:
2905:
2769:
2530:
2509:
2485:
2467:
2165:
2133:
1951:{\displaystyle 1/n}
1919:
1824:
1792:
1764:{\displaystyle q=0}
1738:{\displaystyle q=1}
1705:
1687:
1664:
1649:
1554:
1536:
1513:
1455:
1415:
1252:{\displaystyle 1-q}
1213:. If the fraction
1202:
1170:
891:Accounting scandals
881:Stock market bubble
601:Government spending
558:Employment contract
510:Corporate tax haven
269:Credit default swap
6625:Structured product
6620:Structured finance
6600:Speculative attack
6286:Cash flow matching
6249:Non-financial risk
6146:Interest rate risk
6072:Concentration risk
5867:Journal of Finance
5594:98, 1963, 108-113.
5556:2015-04-02 at the
5436:2017-03-31 at the
5339:O'Sullivan, Arthur
5310:Outline of finance
5281:
5212:Merchant of Venice
4878:
4835:
4834:
4796:
4726:
4698:
4678:
4654:
4637:
4611:
4581:
4539:
4452:
4409:
4389:
4318:
4298:
4278:
4248:
4228:
4213:
4193:
4088:
4073:
4034:
4014:
4013:
3993:
3812:
3796:
3790:
3711:
3672:
3652:
3428:
3379:
3359:
3184:
3164:
3053:
3030:
2891:
2871:
2830:
2771:
2755:
2749:
2697:
2677:
2647:
2534:
2516:
2495:
2471:
2453:
2380:
2261:
2194:
2174:
2151:
2134:
2119:
2075:
1948:
1920:
1905:
1888:
1865:
1845:
1825:
1810:
1793:
1778:
1761:
1735:
1709:
1691:
1673:
1650:
1635:
1618:
1598:
1578:
1558:
1540:
1522:
1499:
1476:
1456:
1441:
1401:
1333:
1313:
1293:
1249:
1223:
1203:
1188:
1171:
1156:
1139:
1119:
886:Stock market crash
736:Investment banking
726:Fractional-reserve
691:Warrant of payment
640:Government revenue
563:Financial planning
481:Structured finance
18:Concentrated stock
6666:
6665:
6438:Corporate finance
6433:Capital structure
6387:Cash flow at risk
6383:Liquidity at risk
6356:Survival analysis
6257:
6256:
6203:Reputational risk
6077:Credit derivative
5976:William F. Sharpe
5933:Kenneth L. Fisher
5641:978-0-15-504266-7
5586:Samuelson, Paul,
5569:Samuelson, Paul,
5183:, in the book of
5133:
5132:
4863:
4819:
4781:
4769:
4736:
4724:
4664:
4569:
4527:
4515:
4505:
4462:
4446:
4442:
4372:
4321:{\displaystyle j}
4301:{\displaystyle i}
4251:{\displaystyle i}
3892:
3890:
3728:
3726:
2727:
2722:
2720:
2700:{\displaystyle i}
2400:
2197:{\displaystyle n}
1968:
1891:{\displaystyle n}
1868:{\displaystyle y}
1848:{\displaystyle x}
1621:{\displaystyle q}
1601:{\displaystyle 1}
1581:{\displaystyle 0}
1479:{\displaystyle q}
1353:
1336:{\displaystyle y}
1316:{\displaystyle x}
1226:{\displaystyle q}
1142:{\displaystyle y}
1122:{\displaystyle x}
964:
963:
854:
853:
804:
803:
792:Deposit insurance
698:
697:
532:
531:
430:Corporate finance
425:Capital structure
420:Capital budgeting
355:Performance bonds
236:
235:
219:Financial centres
179:Financial planner
79:Asset (economics)
16:(Redirected from
6686:
6540:Growth investing
6458:Enterprise value
6408:Asset allocation
6391:Earnings at risk
6373:and extensions (
6316:Market portfolio
6180:Operational risk
6165:Refinancing risk
6040:
6039:
6018:
6011:
6004:
5995:
5994:
5960:
5949:
5943:
5930:
5924:
5913:
5907:
5897:
5891:
5890:
5862:
5856:
5851:
5845:
5842:
5836:
5835:
5811:
5805:
5804:
5802:
5801:
5792:. Archived from
5786:
5780:
5779:
5763:
5754:
5748:
5747:
5739:
5733:
5732:
5712:
5706:
5705:
5693:
5687:
5686:
5684:
5683:
5674:. Archived from
5667:
5661:
5652:
5646:
5645:
5633:
5619:
5613:
5601:
5595:
5584:
5578:
5567:
5561:
5547:
5541:
5530:
5524:
5523:
5491:
5485:
5484:
5468:
5458:
5452:
5447:
5441:
5427:
5421:
5420:
5418:
5417:
5412:
5405:
5401:
5395:
5394:
5392:
5391:
5385:
5379:. Archived from
5378:
5371:
5367:
5361:
5360:
5335:
4977:
4976:
4970:=30 is close to
4932:overdiversifying
4887:
4885:
4884:
4879:
4874:
4873:
4865:
4864:
4856:
4848:
4843:
4833:
4805:
4803:
4802:
4797:
4792:
4791:
4783:
4782:
4774:
4770:
4765:
4754:
4748:
4743:
4738:
4737:
4729:
4725:
4717:
4711:
4706:
4687:
4685:
4684:
4679:
4676:
4671:
4666:
4665:
4657:
4646:
4644:
4643:
4638:
4620:
4618:
4617:
4612:
4610:
4609:
4590:
4588:
4587:
4582:
4580:
4579:
4571:
4570:
4562:
4548:
4546:
4545:
4540:
4538:
4537:
4529:
4528:
4520:
4516:
4508:
4506:
4498:
4474:
4469:
4464:
4463:
4455:
4451:
4444:
4443:
4441:
4440:
4428:
4422:
4417:
4398:
4396:
4395:
4390:
4373:
4365:
4360:
4359:
4347:
4346:
4327:
4325:
4324:
4319:
4307:
4305:
4304:
4299:
4287:
4285:
4284:
4279:
4277:
4276:
4257:
4255:
4254:
4249:
4237:
4235:
4234:
4229:
4226:
4221:
4202:
4200:
4199:
4194:
4192:
4191:
4179:
4178:
4169:
4168:
4158:
4153:
4125:
4120:
4101:
4096:
4086:
4081:
4071:
4066:
4047:
4042:
4023:
4021:
4020:
4015:
4012:
4011:
4010:
3994:
3989:
3988:
3984:
3977:
3976:
3964:
3956:
3955:
3937:
3936:
3924:
3916:
3915:
3898:
3889:
3888:
3879:
3878:
3868:
3863:
3835:
3830:
3811:
3809:
3804:
3791:
3786:
3785:
3784:
3779:
3775:
3771:
3770:
3758:
3750:
3749:
3734:
3724:
3719:
3709:
3704:
3685:
3680:
3661:
3659:
3658:
3653:
3651:
3647:
3640:
3639:
3627:
3619:
3618:
3600:
3599:
3587:
3579:
3578:
3566:
3565:
3556:
3555:
3545:
3540:
3512:
3507:
3489:
3488:
3476:
3475:
3463:
3455:
3454:
3441:
3436:
3426:
3421:
3401:
3392:
3387:
3368:
3366:
3365:
3360:
3358:
3354:
3347:
3346:
3334:
3326:
3325:
3307:
3306:
3294:
3286:
3285:
3273:
3272:
3263:
3262:
3252:
3247:
3231:
3226:
3206:
3197:
3192:
3173:
3171:
3170:
3165:
3163:
3162:
3157:
3153:
3146:
3145:
3133:
3125:
3124:
3112:
3111:
3101:
3096:
3075:
3066:
3061:
3039:
3037:
3036:
3031:
3026:
3025:
3020:
3016:
3012:
3011:
2999:
2994:
2993:
2983:
2978:
2960:
2959:
2950:
2949:
2939:
2934:
2913:
2904:
2899:
2880:
2878:
2877:
2872:
2867:
2866:
2854:
2839:
2837:
2836:
2831:
2826:
2825:
2813:
2812:
2800:
2792:
2791:
2779:
2770:
2768:
2763:
2750:
2745:
2741:
2740:
2728:
2725:
2706:
2704:
2703:
2698:
2686:
2684:
2683:
2678:
2676:
2675:
2656:
2654:
2653:
2648:
2643:
2642:
2630:
2625:
2624:
2614:
2609:
2588:
2587:
2575:
2543:
2541:
2540:
2535:
2529:
2524:
2508:
2503:
2484:
2479:
2466:
2461:
2446:
2445:
2427:
2426:
2414:
2413:
2401:
2398:
2389:
2387:
2386:
2381:
2376:
2375:
2360:
2334:
2333:
2318:
2304:
2303:
2288:
2270:
2268:
2267:
2262:
2260:
2259:
2241:
2240:
2228:
2227:
2203:
2201:
2200:
2195:
2183:
2181:
2180:
2175:
2170:
2164:
2159:
2143:
2141:
2140:
2135:
2132:
2127:
2115:
2114:
2105:
2084:
2082:
2081:
2076:
2071:
2070:
2055:
2029:
2028:
2013:
1999:
1998:
1983:
1969:
1966:
1957:
1955:
1954:
1949:
1944:
1929:
1927:
1926:
1921:
1918:
1913:
1897:
1895:
1894:
1889:
1874:
1872:
1871:
1866:
1854:
1852:
1851:
1846:
1834:
1832:
1831:
1826:
1823:
1818:
1802:
1800:
1799:
1794:
1791:
1786:
1770:
1768:
1767:
1762:
1744:
1742:
1741:
1736:
1718:
1716:
1715:
1710:
1704:
1699:
1686:
1681:
1669:
1663:
1658:
1648:
1643:
1627:
1625:
1624:
1619:
1607:
1605:
1604:
1599:
1587:
1585:
1584:
1579:
1567:
1565:
1564:
1559:
1553:
1548:
1535:
1530:
1518:
1512:
1507:
1485:
1483:
1482:
1477:
1465:
1463:
1462:
1457:
1454:
1449:
1440:
1439:
1414:
1409:
1400:
1399:
1354:
1351:
1342:
1340:
1339:
1334:
1322:
1320:
1319:
1314:
1302:
1300:
1299:
1294:
1258:
1256:
1255:
1250:
1232:
1230:
1229:
1224:
1212:
1210:
1209:
1204:
1201:
1196:
1180:
1178:
1177:
1172:
1169:
1164:
1148:
1146:
1145:
1140:
1128:
1126:
1125:
1120:
1063:market portfolio
1030:emerging markets
996:weighted average
986:in a variety of
956:
949:
942:
928:Money portal
926:
925:
924:
914:
913:
864:Economic history
826:
825:
759:
758:
657:Deficit spending
631:Transfer payment
597:
596:
525:Transfer pricing
471:Leveraged buyout
445:Enterprise value
399:
398:
314:Letter of credit
299:Futures contract
132:
130:Over-the-counter
119:Foreign exchange
66:
65:
53:
30:
29:
21:
6694:
6693:
6689:
6688:
6687:
6685:
6684:
6683:
6669:
6668:
6667:
6662:
6639:
6575:Systematic risk
6473:Expected return
6453:Economic bubble
6448:Diversification
6443:Cost of capital
6396:
6253:
6222:
6174:
6156:Volatility risk
6120:Price area risk
6086:
6062:Settlement risk
6031:
6022:
5968:
5963:
5950:
5946:
5931:
5927:
5914:
5910:
5898:
5894:
5879:10.2307/2975974
5863:
5859:
5852:
5848:
5843:
5839:
5812:
5808:
5799:
5797:
5788:
5787:
5783:
5776:
5756:
5755:
5751:
5740:
5736:
5713:
5709:
5694:
5690:
5681:
5679:
5672:"Risk and Time"
5668:
5664:
5653:
5649:
5642:
5624:Fama, Eugene F.
5620:
5616:
5603:Ross, Stephen,
5602:
5598:
5585:
5581:
5568:
5564:
5558:Wayback Machine
5549:Schoen, Robert
5548:
5544:
5532:Asness, Cliff;
5531:
5527:
5512:10.2307/2330969
5492:
5488:
5481:
5459:
5455:
5448:
5444:
5438:Wayback Machine
5428:
5424:
5415:
5413:
5410:
5406:
5403:
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5389:
5387:
5383:
5376:
5372:
5369:
5368:
5364:
5357:
5336:
5332:
5328:
5320:Systematic risk
5269:
5257:value investing
5242:Markowitz model
5234:Harry Markowitz
5177:
5151:
5138:
4966:The result for
4944:
4906:systematic risk
4897:
4866:
4855:
4854:
4853:
4844:
4839:
4823:
4817:
4814:
4813:
4784:
4773:
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4755:
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4097:
4092:
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4032:
4029:
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4003:
3999:
3995:
3972:
3968:
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3903:
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3667:
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3631:
3623:
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3595:
3591:
3583:
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3570:
3561:
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3497:
3484:
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3471:
3467:
3459:
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3437:
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3258:
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3211:
3207:
3202:
3193:
3188:
3182:
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3158:
3141:
3137:
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3120:
3116:
3107:
3103:
3097:
3086:
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3071:
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3057:
3051:
3048:
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3021:
3007:
3003:
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2989:
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2979:
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2951:
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2935:
2924:
2919:
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2909:
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2895:
2889:
2886:
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2862:
2858:
2850:
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2821:
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2796:
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2775:
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2751:
2736:
2732:
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2721:
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2692:
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2599:
2583:
2579:
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2566:
2565:
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2525:
2520:
2504:
2499:
2480:
2475:
2462:
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2441:
2437:
2422:
2418:
2409:
2405:
2397:
2395:
2392:
2391:
2371:
2367:
2356:
2329:
2325:
2314:
2299:
2295:
2284:
2276:
2273:
2272:
2255:
2251:
2236:
2232:
2223:
2219:
2217:
2214:
2213:
2189:
2186:
2185:
2166:
2160:
2155:
2149:
2146:
2145:
2128:
2123:
2110:
2106:
2101:
2090:
2087:
2086:
2066:
2062:
2051:
2024:
2020:
2009:
1994:
1990:
1979:
1965:
1963:
1960:
1959:
1940:
1935:
1932:
1931:
1914:
1909:
1903:
1900:
1899:
1883:
1880:
1879:
1860:
1857:
1856:
1840:
1837:
1836:
1819:
1814:
1808:
1805:
1804:
1787:
1782:
1776:
1773:
1772:
1750:
1747:
1746:
1724:
1721:
1720:
1700:
1695:
1682:
1677:
1665:
1659:
1654:
1644:
1639:
1633:
1630:
1629:
1613:
1610:
1609:
1593:
1590:
1589:
1573:
1570:
1569:
1549:
1544:
1531:
1526:
1514:
1508:
1503:
1491:
1488:
1487:
1471:
1468:
1467:
1450:
1445:
1435:
1431:
1410:
1405:
1395:
1391:
1350:
1348:
1345:
1344:
1328:
1325:
1324:
1308:
1305:
1304:
1264:
1261:
1260:
1238:
1235:
1234:
1218:
1215:
1214:
1197:
1192:
1186:
1183:
1182:
1165:
1160:
1154:
1151:
1150:
1134:
1131:
1130:
1114:
1111:
1110:
1094:
1055:
1046:expected return
1038:
1011:
972:diversification
960:
922:
920:
908:
896:
895:
866:
856:
855:
847:Fund governance
823:
806:
805:
772:Banking license
763:Bank regulation
750:
721:Deposit account
710:
700:
699:
686:Non-tax revenue
682:
661:
627:
594:
584:
583:
580:
544:
534:
533:
486:Venture capital
450:Risk management
396:
386:
385:
384:
375:Syndicated loan
351:
248:
238:
237:
128:
63:
28:
23:
22:
15:
12:
11:
5:
6692:
6682:
6681:
6664:
6663:
6661:
6660:
6655:
6650:
6644:
6641:
6640:
6638:
6637:
6632:
6627:
6622:
6617:
6612:
6607:
6602:
6597:
6592:
6587:
6582:
6577:
6572:
6567:
6562:
6557:
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6547:
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6505:
6500:
6495:
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6455:
6450:
6445:
6440:
6435:
6430:
6425:
6420:
6415:
6410:
6404:
6402:
6401:Basic concepts
6398:
6397:
6395:
6394:
6379:Margin at risk
6375:Profit at risk
6368:
6366:Tracking error
6363:
6353:
6348:
6343:
6338:
6336:Risk-free rate
6333:
6328:
6323:
6318:
6313:
6308:
6303:
6298:
6293:
6288:
6283:
6278:
6273:
6267:
6265:
6259:
6258:
6255:
6254:
6252:
6251:
6246:
6241:
6236:
6234:Execution risk
6230:
6228:
6224:
6223:
6221:
6220:
6215:
6213:Political risk
6210:
6205:
6200:
6195:
6190:
6184:
6182:
6176:
6175:
6173:
6172:
6161:Liquidity risk
6158:
6153:
6151:Inflation risk
6148:
6143:
6141:Margining risk
6138:
6133:
6131:Valuation risk
6128:
6123:
6100:Commodity risk
6096:
6094:
6088:
6087:
6085:
6084:
6082:Securitization
6079:
6074:
6069:
6064:
6059:
6054:
6048:
6046:
6037:
6033:
6032:
6025:Financial risk
6021:
6020:
6013:
6006:
5998:
5992:
5991:
5982:
5967:
5966:External links
5964:
5962:
5961:
5944:
5925:
5908:
5892:
5857:
5846:
5837:
5806:
5781:
5774:
5749:
5744:InvestmentNews
5734:
5707:
5688:
5662:
5647:
5640:
5614:
5596:
5579:
5562:
5542:
5534:David Kabiller
5525:
5506:(3): 353–363.
5486:
5479:
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5442:
5422:
5396:
5362:
5355:
5329:
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5265:
5230:
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5220:
5196:
5195:
5192:
5176:
5173:
5165:Paul Samuelson
5150:
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4777:
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2250:
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2193:
2173:
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2023:
2019:
2016:
2012:
2008:
2005:
2002:
1997:
1993:
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1248:
1245:
1242:
1222:
1200:
1195:
1191:
1168:
1163:
1159:
1138:
1118:
1098:financial risk
1093:
1090:
1054:
1051:
1037:
1034:
1010:
1007:
962:
961:
959:
958:
951:
944:
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779:
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766:
765:
757:
756:
754:Lists of banks
749:
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743:
738:
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728:
723:
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675:
664:
662:
660:
659:
654:
648:
643:
642:
636:
635:
634:
633:
628:
626:
625:
623:Redistribution
620:
614:
612:
604:
603:
595:
590:
589:
586:
585:
582:
581:
579:
578:
573:
567:
565:
560:
555:
545:
540:
539:
536:
535:
530:
529:
528:
527:
522:
517:
512:
507:
498:
497:
491:
490:
489:
488:
483:
478:
473:
465:
464:
460:
459:
458:
457:
452:
447:
442:
437:
432:
427:
422:
417:
412:
404:
403:
397:
392:
391:
388:
387:
383:
382:
377:
372:
367:
362:
357:
350:
349:
343:
338:
328:
327:
326:
321:
316:
311:
306:
301:
296:
291:
286:
281:
271:
266:
261:
256:
250:
249:
244:
243:
240:
239:
234:
233:
232:
231:
226:
221:
213:
212:
206:
205:
204:
203:
198:
193:
192:
191:
181:
176:
171:
169:Angel investor
163:
162:
156:
155:
154:
153:
148:
143:
138:
136:Private equity
133:
126:
121:
116:
111:
106:
101:
96:
91:
86:
81:
73:
72:
64:
59:
58:
55:
54:
46:
45:
39:
38:
26:
9:
6:
4:
3:
2:
6691:
6680:
6677:
6676:
6674:
6659:
6656:
6654:
6651:
6649:
6646:
6645:
6642:
6636:
6633:
6631:
6630:Systemic risk
6628:
6626:
6623:
6621:
6618:
6616:
6613:
6611:
6608:
6606:
6603:
6601:
6598:
6596:
6593:
6591:
6588:
6586:
6583:
6581:
6578:
6576:
6573:
6571:
6568:
6566:
6563:
6561:
6558:
6556:
6553:
6551:
6548:
6546:
6543:
6541:
6538:
6536:
6533:
6529:
6526:
6524:
6521:
6519:
6516:
6514:
6511:
6509:
6506:
6504:
6501:
6499:
6496:
6494:
6491:
6489:
6486:
6484:
6481:
6480:
6479:
6476:
6474:
6471:
6469:
6466:
6464:
6461:
6459:
6456:
6454:
6451:
6449:
6446:
6444:
6441:
6439:
6436:
6434:
6431:
6429:
6428:Capital asset
6426:
6424:
6421:
6419:
6418:Asset pricing
6416:
6414:
6411:
6409:
6406:
6405:
6403:
6399:
6392:
6388:
6384:
6380:
6376:
6372:
6369:
6367:
6364:
6361:
6357:
6354:
6352:
6351:Sortino ratio
6349:
6347:
6344:
6342:
6339:
6337:
6334:
6332:
6329:
6327:
6324:
6322:
6319:
6317:
6314:
6312:
6309:
6307:
6304:
6302:
6299:
6297:
6294:
6292:
6289:
6287:
6284:
6282:
6279:
6277:
6274:
6272:
6269:
6268:
6266:
6264:
6260:
6250:
6247:
6245:
6244:Systemic risk
6242:
6240:
6237:
6235:
6232:
6231:
6229:
6225:
6219:
6216:
6214:
6211:
6209:
6206:
6204:
6201:
6199:
6196:
6194:
6193:Business risk
6191:
6189:
6186:
6185:
6183:
6181:
6177:
6170:
6166:
6162:
6159:
6157:
6154:
6152:
6149:
6147:
6144:
6142:
6139:
6137:
6134:
6132:
6129:
6127:
6124:
6121:
6117:
6113:
6109:
6105:
6101:
6098:
6097:
6095:
6093:
6089:
6083:
6080:
6078:
6075:
6073:
6070:
6068:
6065:
6063:
6060:
6058:
6055:
6053:
6050:
6049:
6047:
6045:
6041:
6038:
6034:
6030:
6026:
6019:
6014:
6012:
6007:
6005:
6000:
5999:
5996:
5990:
5986:
5983:
5981:
5977:
5973:
5970:
5969:
5958:
5954:
5948:
5942:
5941:9780470139516
5938:
5934:
5929:
5922:
5921:9780230288775
5918:
5912:
5906:
5902:
5896:
5888:
5884:
5880:
5876:
5872:
5868:
5861:
5855:
5850:
5841:
5833:
5829:
5825:
5821:
5817:
5810:
5796:on 2011-07-18
5795:
5791:
5785:
5777:
5775:0-8423-3267-7
5771:
5767:
5762:
5761:
5753:
5745:
5738:
5730:
5726:
5722:
5718:
5711:
5704:(4): 108–113.
5703:
5699:
5692:
5678:on 2017-09-11
5677:
5673:
5666:
5659:
5658:
5651:
5643:
5637:
5632:
5631:
5625:
5618:
5611:
5610:
5606:
5600:
5593:
5589:
5583:
5576:
5572:
5566:
5559:
5555:
5552:
5546:
5539:
5535:
5529:
5521:
5517:
5513:
5509:
5505:
5501:
5497:
5490:
5482:
5480:9780870946189
5476:
5472:
5467:
5466:
5457:
5451:
5446:
5439:
5435:
5432:
5426:
5409:
5400:
5386:on 2010-05-08
5382:
5375:
5366:
5358:
5356:0-13-063085-3
5352:
5348:
5344:
5340:
5334:
5330:
5321:
5318:
5316:
5313:
5311:
5308:
5306:
5303:
5301:
5298:
5296:
5293:
5291:
5288:
5286:
5283:
5282:
5279:
5278:
5273:
5264:
5262:
5258:
5254:
5250:
5245:
5243:
5239:
5235:
5227:
5224:
5221:
5218:
5217:
5216:
5214:
5213:
5207:
5205:
5201:
5193:
5190:
5189:
5188:
5186:
5182:
5172:
5170:
5166:
5160:
5155:
5146:
5142:
5128:
5125:
5122:
5121:
5117:
5114:
5111:
5110:
5106:
5103:
5100:
5099:
5095:
5092:
5089:
5088:
5084:
5081:
5078:
5077:
5073:
5070:
5067:
5066:
5062:
5059:
5056:
5055:
5051:
5048:
5045:
5044:
5040:
5037:
5034:
5033:
5029:
5026:
5023:
5022:
5018:
5015:
5012:
5011:
5007:
5004:
5001:
5000:
4989:
4985:
4982:
4979:
4978:
4975:
4973:
4969:
4964:
4962:
4958:
4953:
4952:Martin Gruber
4949:
4939:
4935:
4933:
4928:
4926:
4922:
4917:
4915:
4911:
4907:
4902:
4892:
4875:
4870:
4867:
4857:
4850:
4845:
4840:
4836:
4824:
4812:
4811:
4810:
4793:
4788:
4785:
4775:
4766:
4762:
4759:
4756:
4750:
4745:
4740:
4730:
4721:
4718:
4713:
4708:
4703:
4699:
4691:
4690:
4689:
4673:
4668:
4658:
4634:
4631:
4628:
4606:
4603:
4599:
4576:
4573:
4563:
4534:
4531:
4521:
4512:
4509:
4502:
4499:
4491:
4488:
4485:
4479:
4476:
4471:
4466:
4456:
4448:
4437:
4433:
4429:
4424:
4419:
4414:
4410:
4402:
4401:
4400:
4386:
4383:
4380:
4374:
4369:
4366:
4361:
4356:
4352:
4348:
4343:
4339:
4329:
4315:
4295:
4273:
4270:
4266:
4245:
4223:
4218:
4214:
4188:
4185:
4181:
4175:
4171:
4165:
4161:
4155:
4150:
4147:
4144:
4141:
4138:
4135:
4132:
4128:
4122:
4117:
4114:
4111:
4107:
4103:
4098:
4093:
4089:
4083:
4078:
4074:
4068:
4063:
4060:
4057:
4053:
4049:
4044:
4039:
4035:
4027:
4026:
4007:
4004:
4000:
3996:
3990:
3985:
3973:
3969:
3957:
3952:
3948:
3933:
3929:
3917:
3912:
3908:
3900:
3885:
3881:
3875:
3871:
3865:
3860:
3857:
3854:
3851:
3848:
3845:
3842:
3838:
3832:
3827:
3824:
3821:
3817:
3813:
3806:
3801:
3797:
3793:
3787:
3781:
3776:
3767:
3763:
3751:
3746:
3742:
3737:
3721:
3716:
3712:
3706:
3701:
3698:
3695:
3691:
3687:
3682:
3677:
3673:
3665:
3664:
3648:
3636:
3632:
3620:
3615:
3611:
3596:
3592:
3580:
3575:
3571:
3562:
3558:
3552:
3548:
3542:
3537:
3534:
3531:
3528:
3525:
3522:
3519:
3515:
3509:
3504:
3501:
3498:
3494:
3490:
3485:
3472:
3468:
3456:
3451:
3447:
3438:
3433:
3429:
3423:
3418:
3415:
3412:
3408:
3403:
3394:
3389:
3384:
3380:
3372:
3371:
3355:
3343:
3339:
3327:
3322:
3318:
3303:
3299:
3287:
3282:
3278:
3269:
3265:
3259:
3255:
3249:
3244:
3241:
3238:
3234:
3228:
3223:
3220:
3217:
3213:
3208:
3199:
3194:
3189:
3185:
3177:
3176:
3159:
3154:
3142:
3138:
3126:
3121:
3117:
3108:
3104:
3098:
3093:
3090:
3087:
3083:
3078:
3068:
3063:
3058:
3054:
3046:
3045:
3044:
3043:Rearranging:
3027:
3022:
3017:
3008:
3004:
2990:
2986:
2980:
2975:
2972:
2969:
2965:
2961:
2956:
2952:
2946:
2942:
2936:
2931:
2928:
2925:
2921:
2916:
2906:
2901:
2896:
2892:
2884:
2883:
2882:
2863:
2859:
2827:
2822:
2809:
2805:
2793:
2788:
2784:
2772:
2765:
2760:
2756:
2752:
2746:
2737:
2733:
2713:
2712:
2711:
2708:
2694:
2672:
2668:
2639:
2635:
2621:
2617:
2611:
2606:
2603:
2600:
2596:
2592:
2584:
2580:
2564:
2563:
2562:
2554:
2551:
2547:
2531:
2526:
2521:
2517:
2513:
2510:
2505:
2500:
2496:
2492:
2489:
2486:
2481:
2476:
2472:
2468:
2463:
2458:
2454:
2450:
2442:
2438:
2434:
2431:
2428:
2423:
2419:
2415:
2410:
2406:
2377:
2372:
2368:
2361:
2357:
2353:
2347:
2344:
2341:
2338:
2335:
2330:
2326:
2319:
2315:
2311:
2305:
2300:
2296:
2289:
2285:
2281:
2256:
2252:
2248:
2245:
2242:
2237:
2233:
2229:
2224:
2220:
2210:
2205:
2191:
2171:
2167:
2161:
2156:
2152:
2129:
2124:
2120:
2111:
2107:
2102:
2098:
2092:
2067:
2063:
2056:
2052:
2048:
2042:
2039:
2036:
2033:
2030:
2025:
2021:
2014:
2010:
2006:
2000:
1995:
1991:
1984:
1980:
1976:
1945:
1941:
1937:
1915:
1910:
1906:
1885:
1876:
1862:
1842:
1820:
1815:
1811:
1788:
1783:
1779:
1758:
1755:
1752:
1732:
1729:
1726:
1701:
1696:
1692:
1688:
1683:
1678:
1674:
1666:
1660:
1655:
1651:
1645:
1640:
1636:
1615:
1595:
1575:
1550:
1545:
1541:
1537:
1532:
1527:
1523:
1515:
1509:
1504:
1500:
1496:
1493:
1473:
1451:
1446:
1442:
1436:
1428:
1425:
1422:
1416:
1411:
1406:
1402:
1396:
1392:
1388:
1382:
1376:
1373:
1370:
1364:
1361:
1358:
1330:
1310:
1290:
1284:
1281:
1278:
1272:
1269:
1266:
1246:
1243:
1240:
1220:
1198:
1193:
1189:
1166:
1161:
1157:
1136:
1116:
1107:
1103:
1099:
1089:
1086:
1082:
1080:
1076:
1072:
1068:
1064:
1059:
1050:
1047:
1043:
1040:If the prior
1033:
1031:
1027:
1022:
1018:
1016:
1006:
1004:
999:
997:
993:
989:
985:
981:
977:
973:
969:
957:
952:
950:
945:
943:
938:
937:
935:
934:
929:
919:
917:
912:
907:
905:
902:
901:
900:
899:
892:
889:
887:
884:
882:
879:
877:
874:
872:
869:
868:
865:
860:
859:
848:
845:
843:
840:
838:
835:
833:
830:
829:
828:
827:
822:
821:Financial law
819:
815:
810:
809:
798:
795:
793:
790:
788:
785:
783:
780:
778:
777:Basel Accords
775:
773:
770:
769:
768:
767:
764:
761:
760:
755:
752:
751:
747:
744:
742:
739:
737:
734:
732:
729:
727:
724:
722:
719:
717:
714:
713:
709:
704:
703:
692:
689:
687:
684:
679:
676:
673:
669:
666:
665:
663:
658:
655:
653:
650:
649:
647:
646:
645:
644:
641:
638:
637:
632:
629:
624:
621:
619:
616:
615:
613:
611:
608:
607:
606:
605:
602:
599:
598:
593:
588:
587:
577:
574:
572:
569:
568:
566:
564:
561:
559:
556:
554:
550:
547:
546:
543:
538:
537:
526:
523:
521:
518:
516:
515:Tax inversion
513:
511:
508:
505:
502:
501:
500:
499:
496:
493:
492:
487:
484:
482:
479:
477:
474:
472:
469:
468:
467:
466:
462:
461:
456:
453:
451:
448:
446:
443:
441:
438:
436:
433:
431:
428:
426:
423:
421:
418:
416:
413:
411:
408:
407:
406:
405:
401:
400:
395:
390:
389:
381:
380:Synthetic CDO
378:
376:
373:
371:
368:
366:
363:
361:
358:
356:
353:
352:
347:
344:
342:
339:
337:
333:
330:
329:
325:
322:
320:
317:
315:
312:
310:
307:
305:
302:
300:
297:
295:
292:
290:
287:
285:
282:
279:
275:
272:
270:
267:
265:
262:
260:
257:
255:
252:
251:
247:
242:
241:
230:
227:
225:
222:
220:
217:
216:
215:
214:
211:
208:
207:
202:
199:
197:
194:
190:
189:institutional
187:
186:
185:
182:
180:
177:
175:
172:
170:
167:
166:
165:
164:
161:
158:
157:
152:
149:
147:
144:
142:
139:
137:
134:
131:
127:
125:
122:
120:
117:
115:
112:
110:
107:
105:
102:
100:
97:
95:
94:Capital asset
92:
90:
87:
85:
82:
80:
77:
76:
75:
74:
71:
68:
67:
62:
57:
56:
52:
48:
47:
44:
41:
40:
36:
32:
31:
19:
6585:Moral hazard
6570:Risk of ruin
6447:
6346:Sharpe ratio
6208:Country risk
6169:Deposit risk
6067:Default risk
5956:
5947:
5928:
5911:
5895:
5873:(1): 77–91.
5870:
5866:
5860:
5853:
5849:
5840:
5826:(2): 71–74.
5823:
5819:
5809:
5798:. Retrieved
5794:the original
5784:
5759:
5752:
5743:
5737:
5723:(3): 18–22.
5720:
5716:
5710:
5701:
5697:
5691:
5680:. Retrieved
5676:the original
5665:
5655:
5650:
5629:
5617:
5607:
5599:
5591:
5582:
5574:
5565:
5545:
5528:
5503:
5499:
5489:
5464:
5456:
5445:
5425:
5414:. Retrieved
5404:(in English)
5399:
5388:. Retrieved
5381:the original
5365:
5346:
5333:
5275:
5246:
5231:
5215:(ca. 1599):
5210:
5208:
5197:
5185:Ecclesiastes
5178:
5162:
5157:
5152:
5143:
5139:
4971:
4967:
4965:
4960:
4956:
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4936:
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4918:
4898:
4890:
4808:
4551:
4330:
4205:
3042:
2842:
2709:
2659:
2560:
2549:
2545:
2208:
2206:
1877:
1095:
1087:
1083:
1070:
1060:
1056:
1042:expectations
1039:
1023:
1019:
1014:
1012:
1000:
971:
965:
817:
746:Money supply
731:Full-reserve
716:Central bank
576:Student loan
551: /
463:Transactions
274:Time deposit
160:Participants
89:Asset growth
6635:Toxic asset
6595:Speculation
6528:social work
6513:engineering
6341:Risk parity
6326:Omega ratio
6239:Profit risk
6126:Equity risk
6104:Volume risk
6092:Market risk
6044:Credit risk
5370:(in French)
5204:real estate
4948:Edwin Elton
4921:S&P 500
4914:market risk
2271:instead of
1079:index funds
284:Credit line
246:Instruments
141:Real estate
104:Derivatives
6218:Legal risk
6198:Model risk
6112:Shape risk
6108:Basis risk
6036:Categories
5800:2010-01-09
5682:2019-05-30
5416:2011-06-15
5390:2009-04-02
5326:References
5141:channels.
2546:increasing
980:volatility
814:Regulation
618:Operations
571:Retirement
410:Accounting
294:Derivative
201:Speculator
33:Part of a
6565:Risk pool
6478:Financial
5261:home bias
5169:Zvi Bodie
4912:risk and
4861:¯
4858:σ
4837:σ
4831:∞
4828:→
4779:¯
4776:σ
4760:−
4734:¯
4731:σ
4700:σ
4662:¯
4659:σ
4632:≠
4600:σ
4567:¯
4564:σ
4525:¯
4522:σ
4489:−
4460:¯
4457:σ
4411:σ
4378:∀
4267:σ
4215:σ
4182:σ
4148:≠
4129:∑
4108:∑
4090:σ
4054:∑
4036:σ
4001:σ
3997:≡
3991:⏟
3958:−
3918:−
3858:≠
3839:∑
3818:∑
3798:σ
3794:≡
3788:⏟
3752:−
3692:∑
3674:σ
3621:−
3581:−
3535:≠
3516:∑
3495:∑
3457:−
3409:∑
3381:σ
3328:−
3288:−
3235:∑
3214:∑
3186:σ
3127:−
3084:∑
3055:σ
2966:∑
2962:−
2922:∑
2893:σ
2794:−
2757:σ
2753:≡
2747:⏟
2597:∑
2544:which is
2518:σ
2497:σ
2490:⋯
2473:σ
2455:σ
2432:⋯
2246:⋯
2153:σ
2121:σ
1907:σ
1812:σ
1780:σ
1693:σ
1675:σ
1652:σ
1637:σ
1542:σ
1524:σ
1501:σ
1443:σ
1426:−
1403:σ
1374:−
1282:−
1244:−
1190:σ
1158:σ
992:portfolio
984:investing
876:Recession
837:ISO 31000
520:Tax haven
394:Corporate
309:Insurance
304:Indemnity
210:Locations
99:Commodity
6673:Category
6488:analysis
6423:Bad debt
6301:Drawdown
6263:Modeling
5974:, Prof.
5923:, p. 316
5698:Scientia
5592:Scientia
5554:Archived
5434:Archived
5345:(2003).
5267:See also
4946:In 1977
1102:variance
1071:pro rata
1009:Examples
652:Taxation
542:Personal
495:Taxation
370:Security
324:Mortgage
184:Investor
6503:betting
6493:analyst
6483:adviser
6136:FX risk
5887:2975974
5520:2330969
5175:History
1104:of the
1003:hedging
968:finance
904:Outline
708:Banking
672:balance
670: (
402:General
334: (
289:Deposit
109:Domains
61:Markets
43:Finance
6545:Hazard
6296:Copula
6163:(e.g.
6102:(e.g.
5939:
5919:
5885:
5772:
5638:
5518:
5477:
5353:
5200:Talmud
4994:49.24%
4552:where
4445:
4206:where
2660:where
2209:adding
1303:. If
1106:return
1075:assets
988:assets
816:
668:Budget
592:Public
549:Credit
506:(BEPS)
341:exotic
332:Option
196:Retail
114:Equity
70:Assets
35:series
6550:Hedge
6508:crime
6498:asset
6331:RAROC
6227:Other
5955:, in
5883:JSTOR
5516:JSTOR
5411:(PDF)
5384:(PDF)
5377:(PDF)
5240:(see
5181:Bible
5129:0.39
5126:19.21
5123:1,000
5118:0.39
5115:19.27
5107:0.39
5104:19.29
5096:0.41
5093:20.20
5085:0.42
5082:20.46
5074:0.42
5071:20.87
5063:0.44
5060:21.68
5052:0.49
5049:23.93
5041:0.51
5038:24.98
5030:0.54
5027:26.64
5019:0.60
5016:29.69
5008:0.76
5005:37.36
4997:1.00
4925:index
415:Audit
365:Stock
151:Stock
124:Money
6560:Risk
6523:risk
6027:and
5937:ISBN
5917:ISBN
5770:ISBN
5766:1024
5636:ISBN
5475:ISBN
5351:ISBN
4950:and
4910:beta
4899:The
4647:and
4621:for
4308:and
4258:and
1855:and
1803:and
1745:and
1588:and
1323:and
1181:and
976:risk
741:Loan
678:Debt
553:Debt
336:call
319:Loan
259:Cash
254:Bond
146:Spot
84:Bond
6518:law
6463:ESG
5903:or
5875:doi
5828:doi
5725:doi
5508:doi
5244:).
5112:500
5101:400
4821:lim
2726:Var
2548:in
2399:var
1967:var
1486:is
1352:var
1100:is
982:by
978:or
966:In
346:put
6675::
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