Finance 320

Fall 2019

(100 points) Due: Professor Sapp

Assignment #1

Thursday, Oct. 10 Historical Return and Risk

Objective: The objective of this assignment is to learn how to obtain basic statistical

measures of portfolio performance using historical data. The assignment is also intended

to let you see for yourself whether the actual investment experience of the past eighty years

accords with our understanding of how risky assets are priced by risk-averse investors.

Sheet 1 of the Excel workbook titled "dataset1.xls" (available on the class web page) contains

monthly returns on three stock portfolios, two bond portfolios, a broad stock index, and one-month

U.S. T-bills for the period 1926-2018. The stock portfolios represent all NYSE/AMEX/NASDAQ

stocks grouped into small, medium, and large categories based on their market capitalization. Their

monthly returns are referred to as SMLSTK, MEDSTK, and LRGSTK, respectively. The bond

portfolios are comprised of investment-grade corporate bonds (CBOND) and U.S. government bonds

(GBOND). The monthly rate of inflation (INFL) is also provided.

1. For the five portfolios of stocks and bonds, T-bills, and inflation calculate the following:

a. Find the arithmetic mean, variance, and standard deviation of monthly returns. Also,

report the annualized mean, assuming monthly compounding, and the annualized

standard deviation.

b. Create a column graph of the average monthly returns, with labels.

c. Use the monthly mean rate of inflation to find the monthly average real return for the

five portfolios of stocks and bonds, and for T-bills. d. Find the geometric mean monthly return for each of the five portfolios of stocks and

bonds. Which series shows the largest difference between the arithmetic and geometric

mean return? Which series shows the smallest? Can you state why?

2. Find the pair-wise covariances (in the form of a covariance matrix) of the five portfolios of

stocks and bonds. 3. Find the pair-wise correlations (in the form of a correlation matrix) of the five portfolios of

stocks and bonds. Which two are most highly correlated? Which two have the lowest

correlation? 4. What is the average monthly risk premium earned by the three stock portfolios and the two

bond portfolios over this period of time? 5. For each portfolio of stocks and bonds use least squares regression to calculate the beta with

respect to the value-weighted portfolio of all U.S. stocks (MARKET). 6. Compare your answers from (4) and (5) for each respective portfolio. What relationship would

you expect to see between betas and risk premiums? Do the numbers agree with your

intuition? 7. First, look up and read about the "Small Firm January Effect" in your textbook. Next, look

for evidence of a January Effect in the data. Specifically, for each of the three stock portfolios,

calculate the average monthly risk premium for the month of January over the sample period. Also calculate the average monthly risk premium for these three portfolios over the

Feb-Dec eleven-month period of the year. Comment on what you observe for each portfolio in

the month of January as opposed to the non-January months.

8. Sheet 2 of the workbook contains data on the five assets analyzed above, as well as twelve

additional assets, over the period 1995-2018. The added assets are: real estate, oil, gold,

timber, venture capital, private equity, hedge funds (energy, emerging markets, macro, and

distress), the Europe Australia Far East index of international stocks (EAFE), and high-yield

corporate bonds.

a. Compute the arithmetic mean return for each of the seventeen assets as well as T-bills.

Sort the mean returns from highest to lowest and create a column graph, with labels.

How do the returns of the twelve new assets compare to the five traditional U.S. stock

and bond portfolios over this time period?

b. Compute the correlation matrix for the seventeen assets, filling in the upper triangle of

the matrix. Which asset shows the highest correlation with energy hedge funds? Which

asset shows the highest correlation with real estate returns? Extract the column of

correlations for LRGSTK, sort these correlations from highest to lowest, and create a

column graph, with labels. Suppose we consider a correlation of 0.70 to be "high." Which

assets have a high correlation with large U.S. stocks and which have a low correlation?

c. 9. Pick one of the seventeen assets and create a graph that illustrates the growth of a dollar

invested in the asset over 1995-2018. For comparison, on the same graph illustrate the

growth of a dollar invested in the composite U.S. stock market series (MARKET) over

this time period. (Use a line graph.) Sheet 3 of the workbook contains monthly stock price data for Widgets Our Way Inc. (WOW).

Use the prices to create a series of monthly returns.

a. Compute the arithmetic mean monthly return. Annualize this number, assuming

monthly compounding. The average annual return on the U.S. stock market was 9.4%

over this time period. If the risk of WOW were similar to that of the market, would this

seem to be a good performing stock based on this return?

b. Create a line graph of the stock price data. Based on this graph, was WOW stock a good

investment over this period of time (1995-2018)?

c. Compute the geometric mean monthly return. Annualize this number, assuming monthly

compounding. Based on this return, would this seem to be a good performing stock? d. Which of the two means, arithmetic or geometric, gives an accurate indication of this

stock's performance over this period of time? Can you explain the discrepancy between

the two measures?