FIN
Chap028

# Ci fairfax has stated that she is seeking a 3 real

• Notes
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c.i. Fairfax has stated that she is seeking a 3% real, after-tax return. Table 28G provides nominal, pre-tax figures, which must be adjusted for both taxes and inflation in order to ascertain which portfolios meet Fairfax’s return objective. A simple solution is to subtract the municipal bond return component from the stated return, then subject the resulting figure to a 35% tax rate, and then add back tax-exempt municipal bond income. This produces a nominal, after-tax return. Finally, subtract 4% percent inflation to arrive at the real, after-tax return. For example, Allocation A has a real after-tax return of 3.4%, calculated as follows: {[0.099 – (0.072 × 0.4)] × (1-0.35)} + (0.072 × 0.4) – 0.04 =3.44% Alternatively, this can be calculated as follows: multiply the taxable returns by their respective allocations, sum these products, adjust for the tax rate, add the result to the product of the nontaxable (municipal bond) return and its allocation, and deduct the inflation rate from this sum. For Allocation A: [(0.045 × 0.10) + (0.13 × 0.20) + (0.15 × 0.10) + (0.15 × 0.10) + (0.10 × 0.10)] × (1 − 0.35)+ [(0.072 × 0.4)] – 0.04 = 3.46% Allocation Return Measure A B C D E Nominal Return 9.9% 11.0% 8.8% 14.4% 10.3% Real After-Tax Return 3.5% 3.1% 2.5% 5.3% 3.5% Table 28G also provides after-tax returns that could be adjusted for inflation and then used to identify those portfolios that meet Fairfax’s return guidelines. Allocations A, B, D, and E meet Fairfax’s real, after-tax return objectives. ii. Fairfax has stated that a worst case return of –10% in any 12-month period would be acceptable. The expected return less two times the portfolio risk (expected standard deviation) is the relevant risk tolerance measure. In this case, three allocations meet the criterion: A, C, and E. Allocation Parameter A B C D E Expected Return 9.9% 11.0% 8.8% 14.4% 10.3% Exp. Std. Deviation 9.4% 12.4% 8.5% 18.1% 10.1% Worst Case Return - 8 . % 9 - 13 . % 8 - 8 . % 2 - 21 . % 8 - 9 . % 9 d. i. The Sharpe Ratio for Allocation D, using the cash equivalent rate of 4.5 percent as the risk-free rate, is: (0.144 - 0.045)/0.181 = 0.547 ii. The two allocations with the best Sharpe Ratios are A and E; the ratio for each of these allocations is 0.574. 28-12

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Chapter 28 - Investment Policy and the Framework of the CFA Institute e.The recommended allocation is A. The allocations that meet both the minimum real, after-tax objective and the maximum risk tolerance objective are A and E. These allocations have identical Sharpe Ratios and both of these allocations have large positions in municipal bonds. However, Allocation E also has a large position in REITs, whereas the comparable equity position for Allocation A is a diversified portfolio of large and small cap domestic stocks. Because of the diversification value of the large and small stock positions in Allocation A, as opposed to the specialized or non-diversified nature of REIT stocks and their limited data history, one would have greater confidence that the expectational data for the large- and small- cap stock portfolios will be realized than for the REIT portfolio.
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• Fall '10
• SMITH
• investment policy, CFA Institute, risk tolerance, time horizon

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