Returns on Alternative Investments

State of the Economy T$-$Bills High Tech Collections U$.$S$.$ Rubber$*$ Market portfolio $2-$Stock Portfolio

Probability

Recession $0\mathrm{.}13\mathrm{.}0\%-29\mathrm{.}5\%24\mathrm{.}5\%3\mathrm{.}5\%-19\mathrm{.}5\%0\mathrm{.}0\%$

Below avg. $0\mathrm{.}23\mathrm{.}0\%-9\mathrm{.}5\%10\mathrm{.}5\%-16\mathrm{.}5\%-5\mathrm{.}5\%0\mathrm{.}0\%$

Average $0\mathrm{.}43\mathrm{.}0\%12\mathrm{.}5\%-1\mathrm{.}0\%0\mathrm{.}5\%7\mathrm{.}5\%0\mathrm{.}0\%$

Above avg. $0\mathrm{.}23\mathrm{.}0\%27\mathrm{.}5\%-5\mathrm{.}0\%38\mathrm{.}5\%22\mathrm{.}5\%0\mathrm{.}0\%$

Boom $0\mathrm{.}13\mathrm{.}0\%42\mathrm{.}5\%-20\mathrm{.}0\%23\mathrm{.}5\%35\mathrm{.}5\%0\mathrm{.}0\%$

Expected Return $-2\mathrm{.}5\%$

Standard Deviation

Coefficient of Variation

Sharpe ratio

Beta $0\mathrm{.}001\mathrm{.}31-0\mathrm{.}500\mathrm{.}881\mathrm{.}000\mathrm{.}41$

Suppose you created a $2-$stock portfolio by investing $$50,000$ in High Tech and $$50,000$ in Collections. $(1)$ Calculate the expected return, the standard deviation, the coefficient of variation, and the Sharpe ratio for this portfolio, and fill in the appropriate blanks in the table.

weight in High Tech $50\%$

weight in Collections $50\%$

State of the economy Port. return

Recession

Below average

Average

Above average

Boom

Portfolio return

Port. std dev

Port. CV

Port. Sharpe ratio

Correlation $=$

High Tech$/$Collections Portfolio

$\%$ in HT Exp. ret. Std$.$ dev.

$0\%$

$10\%$

$20\%$

$30\%$

$40\%$

$50\%$

$60\%$

$70\%$

$80\%$

$90\%$

$100\%$

Using data from number $1$: The yield curve is currently flat; that is$,$ long$-$term Treasury bonds also have a $3\mathrm{.}0\%$ yield. Consequently, Merrill Finch assumes that the risk$-$free rate is $3\mathrm{.}0\%.(2)$ Write out the SML equation, use it to calculate the required rate of return on each alternative.

Risk$-$free rate Risk$-$free rate

Mkt return: rM $8\mathrm{.}0\%$ RPM

RPM: $($rM $-$ rRF$)$ Beta $1$ CAPM

rHT $=$

rM $=$

rUSR $=$

rTbill $=$

rColl $=$

Beta rs

$-1\mathrm{.}00$

$-0\mathrm{.}87$

$-0\mathrm{.}50$

$0\mathrm{.}00$

$0\mathrm{.}50$

$0\mathrm{.}88$

$1\mathrm{.}00$

$1\mathrm{.}31$

$1\mathrm{.}50$

$2\mathrm{.}00$

$(3)$ How do the expected rates of return compare with the required rates of return?

Security Exp. Ret. Req. Ret. Conclusion

High Tech

Market

U$.$S$.$ Rubber

T$-$Bills

Collections

$\backslash$beta p $=$

rP $=$

$(5)$ For a portfolio consisting of $50\%$ High Tech and $50\%$ U$.$S$.$ Rubber?

$\backslash$beta p $=$

rP $=$

$"(6)$ Suppose investors raised their inflation expectations by $3$ percentage points over current estimates as reflected in the $3\mathrm{.}0\%$ risk$-$free rate. What effect would higher inflation have on the SML and on the returns required on high$-$ and low$-$risk securities$?$

$(7)$ Suppose instead that investors$$ risk aversion increased enough to cause the market risk premium to increase by $3$ percentage points. $($Inflation remains constant.$)$ What effect would this have on the SML and on returns of high$-$ and low$-$risk securities$?"$