Question

You can find a spreadsheet containing the historic returns presented in Table 5.2 on the text’s website at www.mhhe.com/bkm. (Look for the link to Chapter 5 material.)

Copy the data for the last 20 years into a new spreadsheet. Analyze the risk-return trade-off that would have characterized portfolios constructed from large stocks and long-term Treasury bonds over the last 20 years. What was the average rate of return and standard deviation of each asset? What was the correlation coefficient of their annual returns? What would have been the average return and standard deviation of portfolios with differing weights in the two assets? For example, consider weights in stocks starting at zero and incrementing by .10 up to a weight of 1. What was the average return and standard deviation of the minimum-variance combination of stocks and bonds?

Short answer

Average	3.5245	4.057
Standard deviation	19.64	8.88
Corr . Coeff. (Stocks bonds)	0.13

The average return on the less risky portfolio of bonds was higher than that of the riskier portfolio of stocks

Step-by-step solution

Explanation on equilibrium

Since these are annual rates and the risk-free rate was quite variable during the sample period of the recent 20 years, the analysis has to be conducted with continuously compounded rates over T-bill rates.

Calculation of average return and standard deviation

To obtain cc rates, we must convert percentage return to decimal. The decimal cc rate, ln (1+percentage rate/100), can then be multiplied by 100 to return to percentage rates.

Excess returns are just the difference between total returns and the risk-free (T bill) rates with cc rates.

Calculation of average return and standard deviation with differing weights

Minimum Variance = 0.1338 0.8662 3.99 8.44

The bond portfolio is less risky, as represented by its lower standard deviation. Yet, as the portfolio table shows, mixing 0.87% of bonds with 13% of stocks would have produced a portfolio less risky than bonds.

In this sample of these 20 years, the average return on the less risky portfolio of bonds was higher than that of the riskier portfolio of stocks.