Question

An investor calculates his return and risk in €. The investor has invested in a U.S. portfolio now worth $1.000. The investor thinks that there is a 40% chance that the portfolio will be worth $1.300 one year from now and a 60% chance that it will be worth $900. The € is now worth $1,07 and the investor thinks that there is a 50% chance that it will be worth $1,00 one year from now and a 50% chance that it will be worth $1,15. What is the expected return on this portfolio, in €'s, and what is the standard deviation of the return, in €'s? (Assume that the return on the portfolio in $ is independent of the $/€ exchange rate).

Answer 1

50% 40% 1300/1.00

60% 900/1.00

50% 40% 1300/1.15

60% 900/1.15

Probability Returns

20% =(1300/1.00)/(1000/1.07)-1=39.100%

30% =(900/1.00)/(1000/1.07)-1=-3.700%

20% =(1300/1.15)/(1000/1.07)-1=20.957%

30% =(900/1.15)/(1000/1.07)-1=-16.261%

Expected return=20%*(39.100%)+30%*(-3.700%)+20%*(20.957%)+30%*(-16.261%)=6.02310%

Standard Deviation=sqrt(20%*(39.100%-6.02310%)^2+30%*(-3.700%-6.02310%)^2+20%*(20.957%-6.02310%)^2+30%*(-16.261%-6.02310%)^2)=20.994%