Guru functionsPortfolio analysis and optimizationPortfolio Management

Black-Litterman Model- Portfolio Allocation And Optimization

Written by Anangsha Saha (Individual Contributor)
Tue Mar 23 2021
black-litterman model
See how MarketXLS helps you take advantage in the markets.
Download Option Templates →
black-litterman model
 

The Black-Litterman Model is a mathematical model used for portfolio allocation and optimisation. It is mainly used by portfolio managers of large investors, like insurance companies and mutual funds, to allocate their resources in various investments and assets. It was developed by Fischer Black and Robert Litterman of Goldman Sachs in 1990.

The BL model combines the Capital Asset Pricing Theory (CAPM) with Bayesian Statistics and the Modern Portfolio Theory to produce efficient estimates of portfolio weights.

Understanding the Modern Portfolio Theory

The modern portfolio theory is a theory on how risk-averse investors can construct portfolios to maximise the expected returns based on a given market risk level. It emphasises that the investor’s risk and returns are not independent observations, but they together influence the portfolio’s overall risk and return. The MPT talks about how investors can construct a diversified portfolio with multiple assets and maximise their returns for a given risk level.

However, the MPT is limited because it can only take into account the available historical market data, and then it uses the same to make assumptions about the future returns.

On the other hand, the Black-Litterman model lets the investor decide upon and apply their own views and risk preferences, and then it optimizes the asset allocation. The BL model improves the asset allocations provided by the MPT by incorporating projections on the future outlook and using pricing models that rely on subjective inputs in addition to objective inputs. However, there is a risk associated with incorporating subjective data as it may result in a biased model. For example, an overly optimistic view of one particular type of asset at a certain point in time may lead to portfolio managers assigning it a higher weight than what the MPT would recommend. If the asset then fails to keep up that momentum, it can result in significant losses, sometimes amounting to hundreds of billions of dollars. 

Structure of the Black-Litterman Model

black-litterman model

black-litterman model

Let us consider a five-asset portfolio model and calculate the expected returns using the Black Litterman model. The user inputs data regarding the (i)global risk premium and risk-free rate, (ii) asset class market capitalisations, (iii) asset class standard deviations, and (iv) asset class correlation. Here we see the results for some sample data using the BL model formulae:

excel

excel

Limitations of the model

  • Assumption of Normality

It is necessary to assume a normal distribution of the market returns. This assumption, in turn, makes the model constrained and reduces its flexibility to adapt to market parameters accurately.

  • Limitations of the market portfolio

The calculations involved in the model rely heavily on the equilibrium portfolio, so any changes in the market portfolio affect the final BL weights. Market equilibrium is tough to define in practice because many risky assets are not taken into account. Thus it is challenging to accurately reproduce the optimal BL allocations using an imperfect market portfolio in the real world.

  • Sensitivity to investor inputs

All portfolio models are affected by the investor’s input data, but the Black-Litterman model is especially sensitive because it contains the added parameter of investor beliefs. The investor has to be careful while trying to input their views into the model because that can easily sway the model’s predictions.

The Bottom Line

The Black-Litterman Model is a robust portfolio allocation algorithm that has broad uses in the finance industry. Despite its mathematical complexity, it simply combines Bayes Rule with the prior, current, and future data and expectations to formulate an optimal portfolio.

One of the Black-Litterman Model’s main advantages is that it allows investors and analysts to incorporate their own beliefs and opinions about the market into the calculations. This makes the BL model robust and reduces its sensitivity to the market dynamics and allows it to efficiently handle the variances of these views.

Disclaimer

None of the content published on marketxls.com constitutes a recommendation that any particular security, portfolio of securities, transaction, or investment strategy is suitable for any specific person. The author is not offering any professional advice of any kind. The reader should consult a professional financial advisor to determine their suitability for any strategies discussed herein. The article is written for helping users collect the required information from various sources deemed to be an authority in their content. The trademarks if any are the property of their owners and no representations are made.

References

faculty.mccombs.utexas.edu › ChileMaterial › Bla…

 

Interested in building, analyzing and managing Portfolios in Excel?
Download our Free Portfolio Template
Download Option Templates

Top 100 Gainers Today

Top 100 losers Today

Real gdpReal personal consumption expReal private investmentReal govt expenditureReal net exportsReal exportsReal importsFederal receiptsFederal outlaysFederal surplus or deficitFederal debtReal private investment nonresidentialReal private investment residentialReal potential gdpReal personal incomeReal personal consumption exp monthlyRpce durable goodsRpce nondurable goodsRpce servicesPersonal savings rateMonetary baseCurrency in circulationBank reservesMoney supply m1Money supply m2Sp500DjiaWilshire indexVixFinancial stress indexCorporate bond index aaCorporate bond index bbbFederal funds rateTreasury rate 3mTreasury rate 1yTreasury rate 5yTreasury rate 10yTips 5yTips 10yBond yield aaaBond yield baaMortgage rate 15yMortgage rate 30yUs dollar weighted averageUsdollar to euroUsdollar to poundYuan to usdollarCanadiandollar to usdollarYen to usdollarCpiCpi wo food energyCpi foodCpi energyChain price indexChain price index wo food energyGdp price deflatorPpi final demandPpi finished goodsPpi materialPpi crude goodsPpi final demand wo food energyPpi finished goods wo food energyHouse price indexHouse price index 20cityCrude oil priceGasoline priceNatural gas priceIndustrial productionCapacity utilisationInventoriesSales retail foodVehicle sales light weightManufacture orders durablesManufacture orders capital goodsLoansConsumer credit outstandingCorporate profitsHousing startsBuilding permitsResidential constructionEmployees nonfarmEmployees privateEmployees goods producingEmployees service providingEmployees governmentUnemployment rateInitial cliamsAverage weeks unemployedJob openingsHiresSeparationsQuitsLayoffs dischargesHours of productionHourly earningsReal outputPopulationLabor forceLabor force participation rate
Search for a stock

Top MarketXLS Rank stocks

Rush Enterprises Inc. Class B Common Stock logo

Rush Enterprises Inc. Class B Common Stock

51.55
 
USD
 
1.94
 
(3.91%)
81
Rank
Optionable: No
Market Cap: 2,753 M
Industry: Auto & Truck Dealerships
52 week range    
35.64   
   57.55
Booz Allen Hamilton Holding Corporation logo

Booz Allen Hamilton Holding Corporation

92.84
 
USD
 
2.48
 
(2.74%)
81
Rank
Optionable: Yes
Market Cap: 11,592 M
Industry: Business Services
52 week range    
69.32   
   93.45
BWX Technologies Inc. logo

BWX Technologies Inc.

56.44
 
USD
 
1.35
 
(2.45%)
80
Rank
Optionable: Yes
Market Cap: 4,846 M
Industry: Aerospace & Defense
52 week range    
42.22   
   61.75
Ritchie Bros. Auctioneers Incorporated logo

Ritchie Bros. Auctioneers Incorporated

67.49
 
USD
 
2.43
 
(3.74%)
77
Rank
Optionable: Yes
Market Cap: 6,928 M
Industry: Business Services
52 week range    
48.44   
   75.28
Ituran Location and Control Ltd. logo

Ituran Location and Control Ltd.

24.33
 
USD
 
-0.16
 
(-0.65%)
77
Rank
Optionable: Yes
Market Cap: 504 M
Industry: Communication Equipment
52 week range    
19.49   
   29.33
General Mills Inc. logo

General Mills Inc.

75.79
 
USD
 
0.34
 
(0.45%)
76
Rank
Optionable: Yes
Market Cap: 42,311 M
Industry: Packaged Foods
52 week range    
55.38   
   75.96
CRA InternationalInc. logo

CRA InternationalInc.

89.15
 
USD
 
-0.17
 
(-0.19%)
76
Rank
Optionable: Yes
Market Cap: 646 M
Industry: Business Services
52 week range    
78.05   
   115.47
ConAgra Brands Inc. logo

ConAgra Brands Inc.

34.56
 
USD
 
0.32
 
(0.93%)
76
Rank
Optionable: Yes
Market Cap: 16,287 M
Industry: Packaged Foods
52 week range    
29.80   
   36.67
Agree Realty Corporation logo

Agree Realty Corporation

73.53
 
USD
 
1.40
 
(1.94%)
76
Rank
Optionable: Yes
Market Cap: 5,522 M
Industry: REIT - Retail
52 week range    
60.78   
   74.67
UNITIL Corporation logo

UNITIL Corporation

61.00
 
USD
 
2.28
 
(3.88%)
75
Rank
Optionable: Yes
Market Cap: 928 M
Industry: Utilities - Diversified
52 week range    
39.90   
   61.08

More Features

Stand with Ukraine

As the situation in Ukraine escalates, many of us in MarketXLS are left with emotions too overwhelming to name. If you’d like to show your support, but aren’t sure how to, we want to help make it easier for you to act.

For any amount donated, we’ll extend your MarketXLS subscription for double of the donated amount. Please send proof of your payment to support@marketxls.com to avail the extention

From all of us at MarketXLS, thank you!