The expected return and standard deviation of SugarKane is now

E(rSugarKane) (.5 7) .3( 5) (.2 20) 6

SugarKane [.5(7 6)2 .3( 5 6)2 .2(20 6)2]1/2 8.72

The covariance between the returns of Best and SugarKane is

Cov(SugarKane, Best) .5(7 6)(25 10.5) .3( 5 6)(10 10.5)

.2(20 6)( 25 10.5) 90.5   and the correlation coefficient is   Cov(SugarKane, Best)

(SugarKane, Best)

SugarKane

Best 90.5 .55 8.72 18.90

The correlation is negative, but less than before ( .55 instead of .86) so we expect that SugarKane will now be a less powerful hedge than before. Investing 50% in SugarKane and 50% in Best will result in a portfolio probability distribu- tion of Probability .5 .3 2

Portfolio return 16 2.5 2.5 resulting in a mean and standard deviation of E(rHedged portfolio) (.5 16) (.3 2.5) .2( 2.5) 8.25

Hedged portfolio [.5(16 - 8.25)2 .3(2.5 - 8.25)2 .2(-2.5 - 8.25)2]1/2 7.94

b. It is obvious that even under these circumstances the hedging strategy dominates the risk-reducing strategy that uses T-bills (which results in E(r) 7.75%, 9.45%). At the same time, the standard deviation of the hedged position (7.94%) is not as low as it was using the original data.

c, d. Using rule 5 for portfolio variance, we would find that   2 (.52 2Best) (.52 2Kane) [2 .5 .5 Cov(SugarKane, Best)]   (.52 18.92) (.52 8.722) [2 .5 .5 (-90.5)] 63.06   which implies that 7.94%, precisely the same result that we obtained by an-