Question

Suppose the risk-free interest rate is 5%, and the stock market will return either 40% or −20% each year, with each outcome equally likely. Compare the following two investment strategies: (1) invest for one year in the risk-free investment, and one year in the market, or (2) invest for both years in the market.

compute the standard deviation for each case B (1) and B (2) and depict all steps in the calculation, that I described.

Answer 1

Expected Market Return = 0.5* 40% + 0.5 * -20% = 10%

SD of market returns = [ 0.5 * (40%-10%)² + 0.5 * (-20%-10%)² ]^1/2 = 30%

Option 1 : Invest one year in risk free and one year in market - This will generate 5% risk free in one year and expected return of 10% in other year with standard deviation of 30%.

So assuming a base investment of 100, the total return for 2 years will be = 100 * (1+5%) * (1+10%) = 115.5. The standard deviation of this portfolio will be - this is like a 2 factor portfolio so we will use the same formula with equal weights :

SD = [(0.5)² * (30%)² + (0.5)²*0 + 2*0.5 * 0.5 * 0] = 15%

Option 2 : investing in the market for both years:

Expected return = 100 * (1+10%)*(1+10%) = 121

SD will be same as market = 30%