1.Consider the following four debt securities, which are identical in every char
ID: 1251368 • Letter: 1
Question
1.Consider the following four debt securities, which are identical in every characteristic except as noted:
?W: A corporate bond rated AAA
?X: A corporate bond rate BBB
?Y: A corporate bond rated AAA with a shorter time to maturity than bonds W and X
?Z: A corporate bond rated AAA with the same time to maturity as bond Y that trades in a more liquid market than bonds W, X, or Y
List the bonds in the most likely order of the interest rates (yields to maturity) of the bonds from highest to lowest. Explain your work.
2.Explain how an economist could use the slope of the yield curve to analyze the probability that a recession will occur and why the spread may matter.
3.One year ago, you bought a bond for $10,000. You received interest of $400 at the end of the year, as well as your $10,000 principal. If the inflation rate over the last year was five percent, calculate the real return. Show your work.
4.Suppose that the price of a stock is $50 at the beginning of a year and $53 at the end of the year, and it pays a dividend of $2 during the year. Calculate the stock’s current yield, capital-gains yield, and the return. Show your work for three separate calculations.
5.Use the capital-asset pricing model to predict the returns next year of the following stocks, if you expect the return to holding stocks to be 12 percent on average, and the interest rate on three-month T-bills will be two percent. Calculate a stock with a beta of -0.3, 0.7, and 1.6. Show your work for three separate calculations.
Explanation / Answer
1. The bond with the highest risk is going to be your BBB bond. A BBB bond is rated at a higher risk and will most likely yield the highest interest rates. BBB bonds fall into what is considered to be a lower medium grade bond and is just above the non-investment grade of bonds. The next below in high risk is going to be your AAA rated bond. AAA bonds are very low in risk in nature depending on their yield to maturity. The AAA bond is placed here because we are unaware of the duration of the bond. That is why the next less risky bond is the AAA bond with a shorter time to maturity than W and X. The reason behind this is that the bond has a less likely chance of its value being diminished. The longer the term, the higher the chance there is that something could happen in the market that could destroy the wealth of the bond. The least risky of the bunch is going to be bond Z that trades in a more liquid market than the others. The reason this is less risky is because there are a larger number of sellers and buyers in this type of market which makes getting rid of an unwanted bond much easier than it would in a less liquid market. So in summary, the highest interest rate would be X as it is a corporate bond with a rating of BBB. The next highest interest rate would be W since it is still a corporate bond but has a better rating of AAA. The next option would be Y since it has a shorter maturity; the interest rate would not be as high because the investor’s money is not locked up as long. The lowest yielding option would be Z since it is actually more liquid than bonds. 2. The yield curve is considered by some to be the best tool to forecast a recession. The yield curve is a "curve" of interest rates for debt certificates. The yield curve demonstrates what interest rates look vs. the maturity. Usually the yield curve is upward sloping since the longer you invest your money, the higher your return should be. However, if the slope is negative (short term rates are higher than long term rates) this may indicate a recession is coming. 3. When you invest money at the current time, there is always a risk that you could actually lose money due to the amount the dollars inflates to over the time of the bond. If you were to invest $2 today and tomorrow the inflation made that $2 worth only $1, depending in the interest rate you receive on the bond, you could end up losing money. The example above on the $10,000 bond is a good example of how inflation can cost you money. The nominal return = (10,400-10,000)/10,000 = 0.04 = 4%. That seems like a respectable rate of return, especially with certificates earning around 1-2% right now. However, this is only the nominal rate of return. We must also subtract the inflation from this since your money isn't worth as much because the price of things have increased. Therefore we subtract 5% (inflation) from your investment return (4%) and you actually lost money (-1%). Although he made money, inflation over the last year has caused his money to be worth less than the original amount. 4. Stock returns have two parts to it, the current yield and the capital gains yield. The current yield deals with the how much money the investor gets paid in dividends. In this example, the investor received $2 of dividends. Since they invested $50, the yield of the dividend was $2/$50 = 4%. The other portion of the total return of a stock is the capital gains yield. In other words, it's the appreciation/depreciation of stock from purchase to sale. In this case the investor purchased the stock for $50 and sold for $53 so they made $53-$50 = $3. To get the rate of return, we must divide this $3 by the initial amount $50 to get, $3/$50 = 6%. Therefore, the total return is 4% + 6% = 10%. The work for these solutions is listed below. 5. For the following three equations, the way I calculated the returns for next year by adding the interest rate of the bond with the beta, which is multiplied by the unsystematic risk minus the interest rate. This equation will give you your return for the following year. Beta of -0.3 = 2% + -0.3(12% - 8%) = 6.8% Beta of 0.7 = 2% + 0.7(12% - 8%) = 10.8% Beta of 1.6 = 2% + 1.6(12% - 8%) = 14.4%
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