Risk and Return in Finance Analysis – Homework Assignment 1

Risk and Return in Finance Analysis Questions

Homework Assignment 1

Chapter 2

1. Suppose you have just inherited $10,000 and are considering the following options for investing the money to maximize your return: Option 1: Put the money in an interest-bearing checking account that earns 2%. The FDIC insures the account against bank failure.

Option 2: Invest the money in a corporate bond with a stated return of 5%, although there is a 10% chance the company could go bankrupt.

Option 3: Loan the money to one of your friend’s roommates, Mike, at an agreed-upon interest rate of 8%, even though you believe there is a 7% chance that Mike will leave town without repaying you.

Option 4: Hold the money in cash and earn zero return. a. If you are risk-neutral (i.e., neither seek out nor shy away from risk), which of the four options should you choose to maximize your expected return? (Hint: To calculate the expected return of an outcome, multiply the probability that an event will occur by the outcome of that event.) b. Suppose Option 3 and Option 4 are your only choices. If you could pay your friend $100 to find out extra information about Mike that would indicate with certainty whether he will leave town without paying, would you pay the $100? What does this say about the value of better information regarding risk?

2. If you were going to get a loan to purchase a new car, which financial intermediary would you use: a credit union, a pension fund, or an investment bank?

3. How can the provision of several types of financial services by one firm be both beneficial and problematic?

4. Why might you be willing to make a loan to your neighbor by putting funds in a savings account earning a 5% interest rate at the bank and having the bank lend her the funds at a 10% interest rate, rather than lend her the funds yourself? 5. If I can buy a car today for $5,000 and it is worth $10,000 in extra income to me next year because it enables me to get a job as a traveling salesman, should I take out a loan from Larry the Loan Shark at a 90% interest rate if no one else will give me a loan? Will I be better or worse off as a result of taking out this loan? Can you make a case for legalizing loan sharking?

Chapter 4

1. To help pay for college, you have just taken out a $1,000 government loan that makes you pay $126 per year for 25 years. However, you don’t have to start making these payments until you graduate from college two years from now. Why is the yield to maturity necessarily less than 12%? (This is the yield to maturity on a normal $1,000 fixed-payment loan on which you pay $126 per year for 25 years.)

2. If mortgage rates rise from 5% to 10%, but the expected rate of increase in housing prices rises from 2% to 9%, are people more or less likely to buy houses?

3. Interest rates were lower in the mid-1980s than in the late 1970s, yet many economists have commented that real interest rates were actually much higher in the mid-1980s than in the late 1970s. Does this make sense? Do you think that these economists are right?

4. Consider a bond with a 4% annual coupon and a face value of $1,000. Complete the following table. What relationships do you observe between years to maturity, yield to maturity, and the current price? Years to Maturity 2 2 3 5 5 Yield to Maturity 2% 4% 4% 2% 6% Current Price

5. What is the price of a perpetuity that has a coupon of $50 per year and a yield to maturity of 2.5%? If the yield to maturity doubles, what will happen to the perpetuity’s price?

6. Suppose that you want to take out a loan and that your local bank wants to charge you an annual real interest rate equal to 3%. Assuming that the annualized expected rate of inflation over the life of the bond is 1%, determine the nominal interest rate that the bank will charge you. What happens if, over the life of the loan, actual inflation is 0.5%?

Chapter 5

1. Suppose you visit with a financial adviser, and you are considering investing some of your wealth in one of three investment portfolios: stocks, bonds, or commodities. Your financial adviser provides you with the following table, which gives the probabilities of possible returns from each investment:

a. Which investment should you choose to maximize your expected return: stocks, bonds, or commodities?

b. If you are risk-averse and have to choose between the stock and the bond investments, which should you choose? Why?

2. An important way in which the Federal Reserve decreases the money supply is by selling bonds to the public. Using a supply and demand analysis for bonds, show what effect this action has on interest rates. Is your answer consistent with what you would expect to find with the liquidity preference framework?

3. Using both the liquidity preference framework and the supply and demand for bonds framework, show why interest rates are procyclical (rising when the economy is expanding and falling during recessions).

4. The demand curve and supply curve for one-year discount bonds with a face value of $1,000 are represented by the following equations Bd: Price = − 0.6 * Quantity + 1,140 Bs: Price = Quantity + 700 Suppose that, as a result of monetary policy actions, the Federal Reserve sells 80 bonds that it holds. Assume that bond demand and money demand are held constant.

a. How does the Federal Reserve policy affect the bond supply equation?

b. Calculate the effect of the Federal Reserve’s action on the equilibrium interest rate in this market.