First calculate the return requirement as N = 20, PV = -$1,500,000, PMT = 0, FV = $3,500,000 → CPT I/Y = 4.33%. Factoring in inflation, this leads to a return requirement of (1.0433 × 1.025) – 1 = 6.90%. We can already eliminate Portfolio 3 since it does not meet the return requirement.
The Anderson’s say they want to maintain $50,000 in cash at all times. Based on their current portfolio value, this leads to a cash percentage of ($50,000 / $1,500,000)= 3.33%. Based on this requirement, we can eliminate Portfolio 1, leaving Portfolio 2 at the best option.
Portfolio 1 looks tempting given its higher return and broad diversification, however, Portfolio 2 has a higher Sharpe ratio. Since the Anderson’s want to get paid for the risk they are taking in the form of expected return, Portfolio 2 is clearly the best option.
Sharpe Ratio Portfolio 1 = (8.62 – 3.0) / 12.80 = 0.439
Sharpe Ratio Portfolio 2 = (7.80 – 3.0) / 10.20 = 0.471
Sharpe Ratio Portfolio 3 = (6.10 – 3.0) / 7.40 = 0.419