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MATHGR5380

Project 1: Long-Only Constrained SAA with Tilts and Annual Rebalancing

Due Date 5/11/2020

Your team must submit a report of up to 3 pages documenting the project and an excel spreadsheet

containing key calculations, following the instructions below. The formula that you used for each calculation

has to be shown for at least one period.

This project has to do with creating and back-testing a long-only SAA portfolio with tilts and annual

rebalancing. There is a set of client constraints that the SAA portfolio has to satisfy. Your investment

universe should comprise a diversified set of assets including US and international equity indices, US and

international bond indices.

You can use the returns and market values for various assets posted on CourseWorks or download your own.

At the minimum, you should backtest 3 annual rebalancings.

Your goals are as follows:

1. Produce annual return forecasts for assets in your investment universe. Apply the Black-

Litterman approach to produce the forecasts by blending equilibrium return forecasts (based on

market values of your assets) with views. Use a risk aversion of 4 in computing the equilibrium

return forecasts. For the view portfolios, establish positive weights for at least one asset, such as US

Small Value equities, for example, and negative for the rest of the assets (market value-weighted) or

for a subset of assets (e.g. US Small Growth equities). Use the He-Litterman paper for guidance as to

the choice of any other parameters and make your level of confidence in your views sufficiently

weak. The weights of your view portfolios should be with the -5% and +5% range.

2. In your spreadsheet, for the final period only, provide:

a. The market capitalization weights and the view portfolio weights [tab name: “Weights”]

b. Your chosen risk aversion, a measure of the strength of your belief in equilibrium, and the

mean and variance associated with your views about the expected returns on the view

portfolios [tab name: “Parameters”]

c. The equilibrium return forecasts and the Black-Litterman blended return forecasts [tab

name: “Return Forecasts”]

3. Estimate your own covariance matrix for each year of your backtest. Please use at least 36 months

of returns to estimate COV for the first year of the back-test and re-estimate it every year by

including 12 more months of the data. Please avoid a look-ahead bias: for each year in the backtest

you can use only the data that existed prior to that year.

4. In your excel spreadsheet, provide the volatility of each asset for each year of your backtest in one

tab labeled “Volatilities” and provide the correlation matrix of the assets, for the final year only, in a

tab labeled “Correlations”.

5. Produce optimized long-only portfolios for each year in your backtest. Use mean-variance

optimization with a risk aversion of 4, the risk model computed in question 3 and the Black-

Litterman forecasts computed in question 1. Impose the following constraints in the optimization:

a. The portfolio is long only

b. Portfolio weights add to 1

In your spreadsheet, in a tab named “BL optimal”, present a chart of the market capitalization weights,

the view portfolio weights and the optimal weights, for each year of your backtest.

6. Backtest the above portfolios assuming annual rebalance and produce the following set of analytics.

Formulas must be given in your spreadsheet:

a. Monthly cumulative returns on your portfolio and the market (use market capitalization

weights and index returns to calculate returns on the market), also presented as an Excel

chart [tab name: “Cumulative”].

b. Monthly drawdowns of your portfolio and the market, also presented as an Excel chart [tab

name: “Drawdowns”]

c. Annualized risk and geometrically annualized return of your portfolio and the market [tab

name: “Total Stats”]

d. Annualized active risk and arithmetically annualized active return of your portfolio (based on

the difference each month between your portfolio’s return and the market return). In other

words, compute tracking error and alpha. From these compute the information ratio of your

portfolio [tab name: “Active Stats”]

e. Geometrically annualized active return of your portfolio (based on the difference between

your portfolio’s geometrically annualized return and the market geometrically annualized

return).

Please describe your work. Your report may contain some of the following points:

• Brief description of the data sources, if you used your own

• Description of the investment universe, if you used your own

• Brief discussion of the tilts that you established

• Black-Litterman: brief description of parameters used

Make sure you use only the information available up to the point in time when you construct your

portfolio each year.

Project grade will not depend on the active returns that your portfolio produced.

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