# Mgtf402 Investment Analysis: Hbs Case Study

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Assignment 1, MgtF402 Investment Analysis (due October 5, 2015)

Part I: HBS case study #5-205-040: Deutsche Bank: Discussing the Equity Risk Premium

The equity risk premium has been described as the single most important variable in finance. It is also very difficult to estimate precisely. This case describes a variety of approaches to determine the equity risk premium. You will get experience with these by using real data from a variety of sources. The excel file Assignment_1_MF402, available from the Assignment 1 folder on TED, has monthly returns on stocks, bonds and T-bills going back to January 1950. The spreadsheet has columns with the date (column A), returns on a value-weighted stock portfolio (column B), returns on 10-year Treasury bonds (column E), and the 3-month T-bill rate (column G). Returns are reported as fractions per month, i.e. 0.05 means five percent. We also show total return indexes (including dividends and coupons) on US stocks, 10-year Treasury bonds and 3-month T-bills in columns C, F and H). These show how \$100 grows over time on a cumulative basis.

1. Using these data, estimate the average excess return on stocks (over the T-bill rate) over the full sample period going back to 1950. You can do this by subtracting the T-bill return column (G) from the stock return column (B). Annualize the monthly mean return figures by multiplying by 12. How precise is your estimate? [Hint: run a regression of excess returns (y-variable) on a constant to get standard errors on the mean excess return (equity risk premium).]

1. How stable is the historical estimate of the equity risk premium over time? [Hint: compute mean returns over a 10-year rolling window (an average over the previous 120 months) and plot this over time.] Comment on your findings.
1. Use the Gordon growth model to estimate the expected return on stocks. Data on the current dividend yield is provided in cell D783 of the Assignment 1 file. (For explanations of this approach, see Section 18.3 in BKM, pages 595-603.) For an estimate of the growth rate of the US economy, see the Survey of Professional Forecasters’ web site at the Federal Reserve Bank of Philadelphia:

http://www.phil.frb.org/research-and-data/real-time-center/survey-of-professional-forecasters/

and click on the third quarter 2015 release.

For an estimate of the real bond yield extracted from 10-year Treasury Inflation-Protected Securities (TIPS), see http://research.stlouisfed.org/fred2/categories/82

1. What estimate of the equity risk premium would you get if you used the ‘novel’ approach on slide 9 of the case study based on the current earnings yield and the real bond yield? The most recent P/E ratio for the Standard & Poor’s 500 index is around 19.85 – the E/P ratio is its inverse (5.0%).

Part II: Calculating Risk measures for stocks and bonds

1. Using the historical data on monthly stock returns and 10-year Treasury bonds from the Assignment_1_MF402 file, estimate the following
1. Sharpe ratio (the monthly mean excess return divided by the monthly standard deviation. Multiply by the square root of 12 to annualize).
2. 5% Value at risk (sort the returns data, then report the fifth percentile of the empirical return distribution).
3. Expected shortfall at α = 5%. (average of returns below 5% Value at Risk cutoff).
4. Skew.
5. Kurtosis.
6. Maximum drawdown over the sample.
7. Do returns appear to be normally distributed?

1. For an investor with a coefficient of risk aversion A = 4, compute the optimal allocation to cash (T-bills), stocks and 10-year T-bonds. Your allocation should use the T-bill rate at the end of the sample as the risk-free rate and sample estimates of the mean, variance and covariance for 10-year Treasury bonds and stocks. [hint: to do this, you can use the formulas on lecture slides 68-72.]
1. The total return indexes in columns C, F and H show the cumulative returns (including dividends or coupons) on US stocks, 10-year Treasury bonds and 3-month T-bills. You can use these to compute the total holding period return over any h-month period as (Indext+h-Indext)/Indext. Use this to answer the following questions:
1. How often (as a percentage of time) did stocks underperform bonds on a monthly basis (h=1)?
2. How often did this happen at the 1-year (h=12), 5-year (h=60) and 10-year horizons (h=120)?
3. How risky are stocks at the 10-year horizon? Plot 10-year cumulated stock returns over time and calculate how often you get a “poor” return and a “lost decade”.
4. Are bonds safer than stocks? How does your answer depend on the investment horizon?
5. Do stocks provide a better inflation hedge than 10-year Treasury bonds? [Hint: compute real stock and bond returns by subtracting the monthly inflation rate in column I from the nominal stock and bond returns. Then study how real stock and bond returns vary with the inflation rate (e.g., using the correlation between returns and inflation at horizons of 1-month (h=1) and 5 years (h=60))].

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