a. (1) Why is T-bill’s return independent of the state of the economy? Do T-bill’s promise a completely risk-free return? Explain
(2) Why are High Tech’s returns expected to move with the economy, whereas, Collections’ are expected to move counter to the economy?
1. The 5.5% T-bill return does not depend on the state of the economy because the Treasury must redeem the bills at par regardless of the state of the economy; therefore, T-bills are risk-free in the default risk sense because the 5.5% return will be realized in all possible economic states. Consequently, this return is composed of the real risk-free rate, (i.e. 3%, plus an inflation premium, say 2.5%). As the economy is …show more content…
Since we have half of our money in each stock, the portfolio’s return will be a weighted average in each type of economy. For a recession, we have: rp = 0.5(-27%) + 0.5(27%) = 0%. We would do similar calculations for the other states of the economy, and get these results:
State | | Portfolio | Recession | | 0.0% | Below average | | 3.0 | Average | | 7.5 | Above average | | 9.5 | Boom | | 12.0 |
Now we can multiply the probability times the outcome in each state to get the expected return on this two-stock portfolio, 6.7%. Alternatively, we could apply this formula, r = wi ri = 0.5(12.4%) + 0.5(1.0%) = 6.7%, which finds r as the weighted average of the expected returns of the individual securities in the portfolio.
It is tempting to find the standard deviation of the portfolio as the weighted average of the standard deviations of the individual securities, as follows: p wi(i) + wj(j) = 0.5(20%) + 0.5(13.2%) = 16.6%.
However, this is not correct—it is necessary to use a different formula, the one for that we used earlier, applied to the two-stock portfolio’s returns. The portfolio’s depends jointly on each security’s and the correlation between the securities’ returns. The best way to approach the problem is to estimate the portfolio’s risk and return in each state of the economy, and then to estimate p with the formula. Given the distribution of returns for the portfolio, we can calculate the portfolios and