CFA L1 Portfolio Construction: practice questions with answers

Question 1

A portfolio is invested 60% in Fund X and 40% in Fund Y. Fund X has an expected return of 9% and a standard deviation of 18%. Fund Y has an expected return of 5% and a standard deviation of 8%. The correlation between the two funds' returns is 0.25. The portfolio's standard deviation is closest to:

1. A 11.26%
2. B 12.01%
3. C 14.00%

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Answer: B. Variance = w1^2 x s1^2 + w2^2 x s2^2 + 2 x w1 x w2 x rho x s1 x s2
= 0.36 x 0.0324 + 0.16 x 0.0064 + 2 x 0.6 x 0.4 x 0.25 x 0.18 x 0.08
= 0.011664 + 0.001024 + 0.001728 = 0.014416.
Standard deviation = 0.014416^0.5 = 12.01%. (The expected return is 0.6 x 9% + 0.4 x 5% = 7.4%.)

Question 2

Dr. Imogen Clarke, aged 38, is a surgeon with a high, stable income, substantial savings and no planned withdrawals for 25 years. During a market fall two years ago she sold all her equities, and she says she cannot sleep when her portfolio loses value. When writing her investment policy statement, her adviser should most appropriately describe her overall risk tolerance as:

1. A below average, because when willingness is lower than ability the more conservative of the two generally governs, although the adviser may try to educate her.
2. B above average, because her ability to bear risk is high and ability always takes precedence over willingness.
3. C average, found by averaging her high ability and low willingness to bear risk.

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Answer: A. Ability to bear risk depends on objective factors such as horizon, wealth, income stability and liquidity needs; Dr. Clarke's is high. Willingness is psychological, and her past behaviour and comments show it is low. When the two conflict, the IPS generally reflects the more conservative measure. The adviser can explain the effects of an overly cautious strategy and try to raise her willingness, but should not simply override it.

Question 3

Wendell Ames holds a portfolio that lies on the capital market line, made up of the market portfolio and the risk-free asset. His portfolio has a standard deviation of 12%, and the market portfolio has a standard deviation of 16%. The beta of Wendell's portfolio is closest to:

1. A 0.56
2. B 0.75
3. C 1.33

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Answer: B. Every portfolio on the capital market line combines the risk-free asset with the market portfolio, so it has no unsystematic risk and its correlation with the market is +1. Beta = rho x sigma(p) / sigma(m) = 1.0 x 0.12 / 0.16 = 0.75. This also equals the weight in the market portfolio: 0.75 x 16% = 12%, and the risk-free asset has a beta of zero. For a CML portfolio, total risk and systematic risk are the same thing.

Question 4

Ingeborg Rask has a portfolio of USD 850,000. She will make no further contributions or withdrawals and wants it to be worth USD 1,200,000 in 8 years, when she plans to buy a vineyard. Ignoring taxes and inflation, the annual compound return objective that should be stated in her investment policy statement is closest to:

1. A 3.6%
2. B 4.4%
3. C 5.1%

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Answer: B. The required return is the compound annual rate that turns the current value into the target: 850,000 x (1 + r)^8 = 1,200,000, so r = (1,200,000 / 850,000)^(1/8) - 1 = (1.41176)^0.125 - 1 = 4.40%. Simply dividing the 41.2% total gain by 8 years (5.1%) overstates the rate needed, because it ignores compounding. In the IPS, this required return is a return objective, and it must be consistent with the client's risk tolerance.

Question 5

After a review, the board of the Calderwood Charitable Foundation concludes that the foundation could not maintain its grant program if its portfolio fell by more than 20% in any year, and it sets this as the maximum loss it is prepared to accept in pursuit of its return goals. This decision is best described as setting the foundation's:

1. A risk budget.
2. B risk transfer policy.
3. C risk tolerance.

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Answer: C. Risk tolerance is the amount of risk an organization is willing and able to accept in pursuit of its goals. It is set by the governing body as part of risk governance, by asking what shortfalls or losses the organization could not bear and how much risk it is prepared to take on. Risk budgeting then allocates that total risk among activities (for example, asset classes or managers). Risk modification methods (prevention/avoidance, acceptance, transfer and shifting) are used to bring actual exposures into line with the tolerance.

Question 6

In the Fama-French three-factor model, a stock's expected excess return is explained by its sensitivity to the market excess return and to two other factors. These two other factors are best described as:

1. A the return on small-cap stocks minus large-cap stocks, and the return on high book-to-market (value) stocks minus low book-to-market (growth) stocks.
2. B the return on past winners minus past losers, and the return on illiquid stocks minus liquid stocks.
3. C unexpected changes in inflation and unexpected changes in industrial production.

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Answer: A. Multifactor return-generating models extend the single-factor market model. The Fama-French three-factor model uses: (1) the market excess return, (2) SMB (small minus big), the return on small-cap stocks minus large-cap stocks, and (3) HML (high minus low), the return on high book-to-market stocks minus low book-to-market stocks. The Carhart model adds a momentum factor; macroeconomic factor models instead use surprises in variables such as GDP growth or inflation.