80:
Black–Litterman overcame this problem by not requiring the user to input estimates of expected return; instead it assumes that the initial expected returns are whatever is required so that the equilibrium asset allocation is equal to what we observe in the markets. The user is only required to state
76:
and covariances of the assets are known. While modern portfolio theory is an important theoretical advance, its application has universally encountered a problem: although the covariances of a few assets can be adequately estimated, it is difficult to come up with reasonable estimates of expected
51:
in practice. The model starts with an asset allocation based on the equilibrium assumption (assets will perform in the future as they have in the past) and then modifies that allocation by taking into account the opinion of the investor regarding future asset performance.
60:
Asset allocation is the decision faced by an investor who must choose how to allocate their portfolio across a number of asset classes. For example, a globally invested pension fund must choose how much to allocate to each major country or region.
81:
how his assumptions about expected returns differ from the markets and to state his degree of confidence in the alternative assumptions. From this, the Black–Litterman method computes the desired (mean-variance efficient) asset allocation.
161:
Black F. and
Litterman R.: Asset Allocation Combining Investor Views with Market Equilibrium, Journal of Fixed Income, September 1991, Vol. 1, No. 2: pp. 7-18
88:
are not allowed – the easiest way to find the optimal portfolio is to use the Black–Litterman model to generate the expected returns for the assets, and then use a
89:
234:
205:
Thomas M. Idzorek: A Step-By-Step Guide to the Black-Litterman Model - Incorporating user-specified confidence levels
166:
Black F. and
Litterman R.: Global Portfolio Optimization, Financial Analysts Journal, September 1992, pp. 28–43
47:, and published in 1992. It seeks to overcome problems that institutional investors have encountered in applying
261:
251:
93:
219:
65:
48:
224:
160:
32:
150:
8:
256:
204:
190:
Guangliang He and Robert
Litterman: The Intuition Behind Black-Litterman Model Portfolios
127:
168:
28:
44:
105:
85:
73:
69:
245:
40:
36:
165:
172:
195:
A. Meucci: The Black-Litterman
Approach: Original Model and Extensions
84:
In general, when there are portfolio constraints – for example, when
199:
194:
189:
20:
225:
Implementation in Python
Notebook and case study analysis
151:
http://www.cis.upenn.edu/~mkearns/finread/intuition.pdf
243:
200:Jay Walters: The Black-Litterman Model in Detail
126:Team, Wallstreetmojo Editorial (2022-09-14).
72:) offers a solution to this problem once the
16:Financial model for portfolio allocation
244:
125:
13:
14:
273:
178:
68:(the mean-variance approach of
144:
119:
1:
216:Spreadsheet implementations:
112:
55:
7:
99:
10:
278:
108:for portfolio optimization
94:constrained optimization
128:"Black Litterman Model"
90:mean-variance optimizer
66:modern portfolio theory
49:modern portfolio theory
35:developed in 1990 at
25:Black–Litterman model
33:portfolio allocation
262:Portfolio theories
29:mathematical model
269:
252:Financial models
153:
148:
142:
141:
139:
138:
123:
74:expected returns
45:Robert Litterman
277:
276:
272:
271:
270:
268:
267:
266:
242:
241:
181:
157:
156:
149:
145:
136:
134:
124:
120:
115:
106:Markowitz model
102:
58:
17:
12:
11:
5:
275:
265:
264:
259:
254:
240:
239:
238:
237:
229:
228:
227:
222:
208:
207:
202:
197:
192:
180:
179:External links
177:
176:
175:
163:
155:
154:
143:
132:WallStreetMojo
117:
116:
114:
111:
110:
109:
101:
98:
57:
54:
15:
9:
6:
4:
3:
2:
274:
263:
260:
258:
255:
253:
250:
249:
247:
236:
233:
232:
230:
226:
223:
221:
218:
217:
215:
214:
213:
212:
206:
203:
201:
198:
196:
193:
191:
188:
187:
186:
185:
174:
170:
167:
164:
162:
159:
158:
152:
147:
133:
129:
122:
118:
107:
104:
103:
97:
95:
92:to solve the
91:
87:
82:
78:
75:
71:
67:
64:In principle
62:
53:
50:
46:
42:
41:Fischer Black
38:
37:Goldman Sachs
34:
30:
26:
22:
210:
209:
183:
182:
146:
135:. Retrieved
131:
121:
83:
79:
63:
59:
24:
18:
220:Peter Ponzo
86:short sales
257:Investment
246:Categories
184:Discussion
137:2022-11-15
113:References
56:Background
235:Canlin Li
231:Applets:
211:Resources
96:problem.
77:returns.
70:Markowitz
100:See also
173:4479577
21:finance
171:
23:, the
169:JSTOR
27:is a
43:and
31:for
39:by
19:In
248::
130:.
140:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.