Question

5. Consider the following Returns Scenario Probability Airline Silver Portfolio (55% airline, 45% silver) Recession Slow Go Normal Boom 1/4 1/4 1/4 1/4 -10 +2 +6 +20 +18 +5 +3 -20 FYI: Expected Return for Individual Stocks: Airline (-10+2+6+20)/4 = 4.5% Silver (+20+5+3-20)/4 = 1.5% Show the expected return, variance and standard deviation of a 55% airline, 45% silver portfolio.

Answer 1

Expected Return of Portfolio (Rp) = (Weight of airline * Expected Return of Airline) + (Weight of Silver * Expected Return of Silver)

Rp = 0.55*4.5% + 0.45*1.5%

Rp = 2.475% + 0.675%

Rp = 3.15%

Hence, Expected return of Portfolio is with 55% airline and 45% silver is 3.15%.

Standard Deviation of Portfolio = Square Root * {(Wa)^2 * (σa)^2 + (Wb)^2 * (σb)^2 + 2*(Wa)*(Wb)*(σa)*(σb)*[Corr(a,b)]}

σp = [(0.55)^2*(3.092%)^2 + (0.45)^2*(3.95%)^2 + 2*(0.55)*(0.45)*(3.092%)*(3.95%)*(-0.98748683)]

σp = 0.2856%

Variance of Portfolio = (σp)^2 = 0.0008156%

Wa = Weightage of Airline stocks in the portfolio

σa = Standard Deviation of Airline Stocks

Wb = Weightage of Silver stocks in the portfolio

σb = Standard Deviation of Silver Stocks

Corr(a,b) = Correlation between Airline and Silver Stocks