Midterm Examination Answers Economics 280, Fall 1999 Wednesday Class

100 points possible, 20 points per question. Average Score 59.98, Standard Deviation 20.13. Maximum = 94, Minimum = 12.

1. Kadesha v. Adam

  1. (13 points) After 1 year, Kadesha earns $30,600. This represents a raise of ($30,600-$30,000)/$30,000 or 2%. Since there was no inflation over the first year that Kadesha worked, the 2% nominal raise is also a 2% real raise. After 1 year, Adam earns $31,200. This represents a raise of ($31,200-$30,000)/$30,000 = 4%. Since there was a 3% inflation over Adam's first year, his real raise amounts to 4%-3% or a 1% real raise. Since Kadesha's real raise was 2%, Kadesha is doing better than Adam as both individuals entered their second year.
  2. (7 points) Kadesha starts the second year with $30,600. There is a 3% inflation over the course of this year. Therefore, to make her no worse off than she was at the start of her second year, she would have to receive a 3% raise at the start of her third year. This amount is calculated as: $30,600x1.03 = $31,518. Or a raise of $31,518-30,600 = $918.

2. Two-year zero coupon bond. Note that there was a mistake on the exam that was corrected via an announcement: The purchase price of the bond at time t should have been $8,858 rather than $8,898.

  1. (6 points) In the given PDV equation, use the values: and rearrange to solve for the yield to maturity, the interest rate i:
  2. (8 points) In the given rate-of-return equation, use the values: and rearrange to solve for the one year rate of return, r, which is given by: r=($9,254-$8858) - 1 = .0443. It is lower than the yield to maturity, .0625.
  3. (6 points) There are two ways to answer this question. One is to ask, what would be the price of the bond with one year left to maturity if the interest rate had remained at .0625. This is the solution to
Since this price is higher than the selling price, $9,254, and interest rates move inversely with price, we may safely conclude that interest rates have risen over the first year that you held this bond. A second approach is to find the interest rate on the bond with one year to maturity that gives a selling price of $9,254. This is found by solving i=($10,000/$9,254)-1 = .08. Since .08 > .0625, we safely conclude that interest rates have risen over the first year you held this bond. Since interest rates rose, and prices move inversely with interest rates, the selling price of your bond has fallen somewhat, and you have suffered a capital loss on your bond investment.

3. (20 points) Keynes’ liquidity preference view of money demand viewed the demand for money as arising from three motives: 1) the transactions motive, 2) the precautionary motive and 3) the speculative motive. (Explain each in further detail). Keynes’ principle contribution was that individuals hold (demand) money for speculative purposes, e.g. they treat money as just another asset. If interest rates are high, but are expected to fall, individuals will demand interest earning assets such as bonds, and demand less money. On the other hand if interest rates are low, but are expected to rise, individuals will delay purchasing interest earning assets and will instead demand to hold more money. The Keynesian liquidity preference view of money demand is sumarized by the following equation:

where Md is money demand, 0<k<1 is the fraction of real income, Y, held in the form of money for transacations and precautionary purposes, 0< { (i) < 1 is the fraction of real wealth, W held in the form of money for speculative purposes (and this fraction varies inversely with the interest rate, i) and P is the price level.

The Monetarist’s modern quantity theory approach (as presented by Milton Friedman) is really extension of the liquidity preference theory of Keynes. The Monetarist theory of money demand is summarized by the equation:

This equation states that the demand for real money balances M/P is a function of real wealth, W, and the difference in expected returns from holding equities (e), bonds (b) and goods, for which the expected return is the expected inflation rate, Ep from the expected return from holding money. The differences between this theory and the Keynesian view are that in the Monetarist theory, more assets are involved (including durable goods), expected returns are considered, and only differences in expected returns from alternative assets relative to returns on money are important in determining the demand for real money balances.

4. Bonds & Stocks & Portfolios

  1. (6 points) The expected return on U.S. government bonds is found by calculating: .25x.02 + .75x.06 = .05. Similarly, the expected return on stocks is: .25x.20+.75x.10=.125
  2. (6 points) Using the variance formula given, and the expected returns, Er, you found in part a, the variance on bonds is calculated as: .25x(.02-.05)2+.75x(.06-.05)2 =.0003. The standard deviation is the square root of the variance = .0173. Similarly, the variance on stocks is calculated as: .25x(.20-.125)2+.75x(.10-.125)2 =.001875, and the standard deviation is: .0433.
  3. (8 points) For this portfolio, if outcome 1 is realized, the portfolio returns: .5x.02+.5x.20 = .11. If outcome 2 is realized, the portfolio returns .5x.06+.5x.10= .08. So the expected return on the portfolio is: .25x.11 + .75x.08 = .0875. To determine if the portfolio is riskier, you have to compare its variance with the variance of either of the two assets by themselves. Using the expected return on the portfolio, the variance on the portfolio is calculated as: .25x(.11-.0875)2+.75x(.08-.0875)2 = .000169. The standard deviation is .013. Since the variance (standard deviation) on the portfolio’s returns are less than for either asset by itself, the portfolio is less risky than these other two assets. The intuition for this result is that the returns on bonds and stocks are slightly negatively correlated in this example, so that when one has a high return, the other has a low return. In such cases, a portfolio of the two assets will serve to reduce the variance in returns, and thereby reduce risk.

 

  1. Term structure
  1. (6 points) According to the expectations theory, the interest rate on two year U.S. treasury bills is an average of the current and future expected 1 year rates: (.06 + .04)/2 = .05.
  2. (6 points) The yield curve is downward sloping, and looks like this:
    3. 







	This is not the normal shape: yield curves are usually upward sloping.
(6 points)  The preferred habitat theory augments the expectations theory with a term premium term, r
n,t , which increases with the term to maturity reflecting the fact that investors must be compensated for holding their money in bonds for longer periods of time. This modification implies that yield curves will generally slope upward, which is consistent with the empirical evidence.