The T-bond return does not depend on the state of the economy because the interest payments will be made and the bond will be redeemed by the federal government, barring global disaster.
The T-bond, since its return is independent of the state of the economy, is risk-free, but only in the nominal sense. An investor is “guaranteed” an 8.0 percent nominal return. However, the real realized return will depend on inflation over the next year. Thus, the real return, which counts most, is uncertain. Also, if interest rates rise, the bond’s price will decline (slightly, for a l-year bond, and if you must sell it to raise cash, you would suffer a slight loss (a large ...view middle of the document...
However, if return distributions are approximately symmetric, then semivariance offers no advantages over variance and [pic], and it is harder to calculate.)
Here is a risk/return comparison of the four alternatives:
|Alternative |CV | [pic] |
|T-bonds |0.00 |8.0% |
|TECO |0.87 |13.5 |
|Gold Hill |1.03 |8.8 |
|S$P 500 |1.10 |15.0 |
For three of the four investments, the higher the risk as measured by the coefficient of variation, the higher the expected rate of return. However, Gold Hill offers a lower return than TECO, but it has greater total risk. (Of course, investors are looking at Gold Hill’s market risk when setting required rates of return, and this causes the apparent anomaly.)
a. Here is the returns distribution of a 50/50 mix portfolio created from TECO and
Gold Hill :
State of the Estimated Return
Economy Prob. TECO Gold Hill Portfolio
|Recession |0.1 |-8.0% |18.0% |5.0% |
|Below average |0.2 |2.0 |23.0 |12.5 |
|Average |0.4 |14.0 |7.0 |10.5 |
|Above average |0.2 |25.0 |-3.0 |11.0 |
|Boom |0.1 |33.0 |2.0 |17.5 |
|Mean | |13.5% |8.8% |11.15% |
|[pic] | |11.7% |9.1% |2.9% |
|CV | |0.87 |1.03 |0.26 |
The estimated portfolio return in each state of the economy is 0.5(TECO k) + 0.5 (GH k). For example, for the recession state, 0.5(-8.0%) + 0.5(18.0%) = 5.0%.
The expected rate of return on the portfolio, [pic]p , is 11.15 percent :
[pic]p = 0.1 (5.0%) + 0.2(12.5%) + 0.4(10.5%) + 0.2(11.0%) + 0.1(17.5%)
Note that the expected rate of return can also be calculated as the weighted average of the expected returns of the portfolio components:
[pic]p = 0.5(13.5%) + 0.5(8.8%) = 11.15%.
The portfolio’s variance is 8.4, its standard deviation is 2.9 percent, and its coefficient of variation is 0.26. Thus, the riskiness of the portfolio, as measured by standard deviation or coefficient of variation, is significantly less than the...