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1. [24 Points] Consider the historical/actual price data for the following four assets given in the

accompanying table. Do not use excel to find the values requested in question (a) – (f).

Date GOOGL 11/1/11 300 12/1/11 323

1/1/12 290 2/1/12 309 3/1/12 321 4/1/12 303 5/1/12 291 6/1/12 290 7/1/12 317 8/1/12 343

STOCK PRICES

MSFT ATT AAPL 21 17 12 21 18 12 24 17 14 26 18 17 26 18 18 26 19 18 24 20 18 25 21 18 24 23 19 25 22 20

  1. Find the realized rate of returns of these four assets for each month.
  2. Compute the average returns, variances, and standard-deviations of these assets over given ten months.
  3. Based on your findings in (b), which asset has the highest mean return? The largest volatility/risk?
  4. Suppose you invested $1000 each in these assets at the beginning (i.e., 11/1/11) and hold it until the end (8/1/12). What would be the dollar value of your investments as of 8/1/12 in these four assets?
  5. Assume now that these four assets each pay $4, $3, $6, and $2 monthly dividends, respectively. If you are selling these assets at the end on 8/1/12 at a price given in the last raw, then what would be the respective HPR of these assets?
  6. Using the ten-month average returns that you find in (b) and assuming that you want to construct an equally-weighted portfolio of these four assets (i.e., N=4), compute the expected rate of return, variance, and standard deviation of your portfolio.
  1. [10 points] Use Figure 5.1 in the text to analyze the effect of the following on the level of real interest rates:
    1. Businesses become more pessimistic about future demand for their products and decide to reduce their capital spending.
    2. Households are induced to save more because of increased uncertainty about their future Social Security benefits.
    3. The Federal Reserve Board undertakes open-market purchases of U.S. Treasury securities in order to increase the supply of money.
  2. [10 points] Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with an 8% coupon (i.e., paid annually) if it is currently selling at par (i.e., $1000) and the probability distribution of its yield to maturity a year from now is as follows: [Hint: Find the price – HPR combination for each state] State of the Economy Probability of state YTM Excellent 0.25 15%

Good 0.45 8% Poor 0.30 -2%

  1. [10 points] The continuously compounded annual return on a stock is normally distributed with a mean of 40% and standard deviation of 30%. Construct a 99%, 95%, and 90% confidence interval such that we should expect its actual return in any particular year to be between these pair of values. Hint: Look at Figure 5.4.
  2. [10 points] During a period of severe inflation, a bond offered a nominal HPR of 50% per year. The inflation rate was 20% per year.
    1. What was the real HPR on the bond over the year using the exact formula or relationship?
    2. Compare this real HPR to the value you will get using the approximation formula.
  3. [10 points] Given $100,000 to invest, what is the expected risk premium in dollars of investing in equities versus risk-free T-bills (U.S. Treasury bills) based on the following table?

Action

Invest in Equities

Invest in risk-free T-bill

7. [12 POINTS] Utility Formula Data

State Probability

Excellent 0.60 Good 0.35 Poor 0.05

Expected Return

1.00

$ $ $ $

Standard Deviation

30% 50% 16% 21%

40,000.00 25,000.00 6,000.00 3,000.00

Investment

1 2 3 4

Expected Return

12% 15% 21% 24%

𝑼=𝑬(𝒓)− 𝟏𝑨𝝈𝟐 𝟐

  1. On the basis of the utility formula above, which investment would you select averse with A = 4?
  2. On the basis of the utility formula above, which investment would you select averse with A = 6?
  3. On the basis of the utility formula above, which investment would you select neutral?

if you were risk if you were risk if you were risk

8. [13 POINTS] Here are some alternative investments you are considering for one year. (i) Bank A promises to pay 8% on your deposit compounded annually. (ii) Bank B promises to pay 8% on your deposit compounded daily. (iii) Bank C promises to pay 8% on your deposit compounded continuously. Compare the effective annual rate (EAR) on these investments.

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