The annualized performance, in U.S. dollars, of the U.S. and European stock indices are:
Return_US = 10% $\sigma$ _US = 16%
Return_europ_e=11% $\sigma$ _euro_pe=18%
Correlation = 0.60
a. What would be the return and risk of a portfolio invested half in the U.S. market and half in the European index?
b. What if the correlation increases to 0.8?

Question

The annualized performance, in U.S. dollars, of the U.S. and European stock indices are:
Return_US = 10%

\sigma

_US = 16%
Return_europ_e=11%

\sigma

_euro_pe=18%
Correlation = 0.60
a. What would be the return and risk of a portfolio invested half in the U.S. market and half in the European index?
b. What if the correlation increases to 0.8?

Quizplus · Accepted Answer

The Answer is a. Return_portfoli_o = 50% Return_US+ 50% Return_europe = 10.5%.

\sigma

²_portfolio=

\left( 0.5 imes \sigma _ { \mathrm { LE } } ight) ^ { 2 } + \left( 0.5 imes \sigma _ { ext {euope } } ight) ^ { 2 } + 2 imes 0.6 imes 0.5 imes 0.5 imes \sigma _ { \mathrm { LE } } imes \sigma _ { ext {euope } } = 231.4

\sigma

_portfolio ₌ _15.21%.
b. The return of the portfolio remains unchanged at 10.5%. The risk is higher at:

\sigma

²_portfolio ₌

\left( 0.5 imes \sigma _ { \mathrm { LE } } ight) ^ { 2 } + \left( 0.5 imes \sigma _ { ext {euope } } ight) ^ { 2 } + 2 imes 0.8 imes 0.5 imes 0.5 imes \sigma _ { \mathrm { LE } } imes \sigma _ { ext {euppe } } = 260.2

\sigma

_portfolio =16.13%.

The Annualized Performance, in U σ\sigmaσ US = 16% Returneurope=11 σ\sigmaσ europe =18% Correlation = 0

The Annualized Performance, in U $\sigma$ _US = 16%
Return_europ_e=11 $\sigma$ _euro_pe=18%
Correlation = 0