Quiz 17: Financial Economics

Suppose that you invest $100 today in a risk-free investment and let the 4 percent annual interest rate compound. Rounded to full dollars, what will be the value of your investment 4 years from now?

Suppose that the city of New York issues bonds to raise money to pay for a new tunnel linking New Jersey and Manhattan. An investor named Susan buys one of the bonds on the same day that the city of New York pays a contractor for completing the first stage of construction. Is Susan making an economic or a financial investment? What about the city of New York?

Suppose that you desire to get a lump sum payment of $100,000 two years from now. Rounded to full dollars, how many current dollars will you have to invest today at a 10 percent interest to accomplish your goal?

What is compound interest? How does it relate to the formula: X dollars today = (1 + i ) t X dollars in t years? What is present value? How does it relate to the formula: X /(1 + i ) t dollars today = X dollars in t years?

Suppose that a risk-free investment will make three future payments of $100 in one year, $100 in two years, and $100 in three years. If the Federal Reserve has set the risk-free interest rate at 8 percent, what is the proper current price of this investment? What is the price of this investment if the Federal Reserve raises the risk-free interest rate to 10 percent?

How do stocks and bonds differ in terms of the future payments that they are expected to make? Which type of investment (stocks or bonds) is considered to be more risky? Given what you know, which investment (stocks or bonds) do you think commonly goes by the nickname "fixed income"?

Consider an asset that costs $120 today. You are going to hold it for 1 year and then sell it. Suppose that there is a 25 percent chance that it will be worth $100 in a year, a 25 percent chance that it will be worth $115 in a year, and a 50 percent chance that it will be worth $140 in a year. What is its average expected rate of return? Next, figure out what the investment's average expected rate of return would be if its current price were $130 today. Does the increase in the current price increase or decrease the asset's average expected rate of return? At what price would the asset have a zero average expected rate of return?

What are mutual funds? What different types of mutual funds are there? And why do you think they are so popular with investors?

Suppose initially that two assets, A and B, will each make a single guaranteed payment of $100 in 1 year. But asset A has a current price of $80 while asset B has a current price of $90.a. What are the rates of return of assets A and B at their current prices? Given these rates of return, which asset should investors buy and which asset should they sell? b. Assume that arbitrage continues until A and B have the same expected rate of return. When arbitrage ends, will A and B have the same price? Next, consider another pair of assets, C and D. Asset C will make a single payment of $150 in one year while D will make a single payment of $200 in one year. Assume that the current price of C is $120 and that the current price of D is $180. c. What are the rates of return of assets C and D at their current prices? Given these rates of return, which asset should investors buy and which asset should they sell? d. Assume that arbitrage continues until C and D have the same expected rate of return. When arbitrage ends, will C and D have the same price? Compare your answers to questions a through d before answering question e. e. We know that arbitrage will equalize rates of return. Does it also guarantee to equalize prices? In what situations will it equalize prices?

Corporations often distribute profits to their shareholders in the form of dividends, which are simply checks mailed out to shareholders. Suppose that you have the chance to buy a share in a fashion company called Rogue Designs for $35 and that the company will pay dividends of $2 per year on that share every year. What is the annual percentage rate of return? Next, suppose that you and other investors could get a 12 percent per year rate of return by owning the stocks of other very similar fashion companies. If investors care only about rates of return, what should happen to the share price of Rogue Designs? (Hint: This is an arbitrage situation.)

Advanced Analysis Suppose that the equation for the SLM is Y = 0.05 + 0.04 X , where Y is the average expected rate of return, 0.05 is the vertical intercept, 0.04 is the slope, and X is the risk level as measured by beta. What is the risk-free interest rate for this SML? What is the average expected rate of return at a beta of 1.5? What is the value of beta at an average expected rate of return is 7 percent?

Why is it reasonable to ignore diversifiable risk and care only about nondiversifiable risk? What about investors who put all their money into only a single risky stock? Can they properly ignore diversifiable risk?

If we compare the betas of various investment opportunities, why do the assets that have higher betas also have higher average expected rates of return?

In this chapter we discussed short-term U.S. government bonds. But the U.S. government also issues longer-term bonds with horizons of up to 30 years. Why do 20-year bonds issued by the U.S. government have lower rates of return than 20-year bonds issued by corporations? And which would you consider more likely, that longer-term U.S. government bonds have a higher interest rate than short-term U.S. government bonds, or vice versa? Explain.

What determines the vertical intercept of the Security Market Line (SML)? What determines its slope? And what will happen to an asset's price if it initially plots onto a point above the SML?

Suppose that the Federal Reserve thinks that a stock market bubble is occurring and wants to reduce stock prices. What should it do to interest rates?

Consider another situation involving the SML. Suppose that the risk-free interest rate stays the same, but that investors' dislike of risk grows more intense. Given this change, will average expected rates of return rise or fall? Next, compare what will happen to the rates of return on low-risk and high-risk investments. Which will have a larger increase in average expected rates of return, investments with high betas or investments with low betas? And will high-beta or low-beta investments show larger percentage changes in their prices?

LAST WORD Why is it so hard for actively managed funds to generate higher rates of return than passively managed index funds having similar levels of risk? Is there a simple way for an actively managed fund to increase its average expected rate of return?