Portfolio Management CFA Level I
question and answers rated A+ 2023
Q. An asset management firm generated the following annual returns in their US large-cap equity
portfolio:
Year Net Return (%)
2008 −34.8
2009 32.2
2010 11.1
2011 −1.4
The 2012 return needed to achieve a trailing five-year geometric mean annualized return of 5% when
calculated at the end of 2012 is closest to:
27.6%.
17.9%.
35.2%. - correct answer C is correct.
R⎯⎯⎯G=0.05=(1−0.348)(1+0.322)(1+0.111)(1−0.014)
(1+R2012)⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√5−1
Holding period total return (cumulative) factor calculation through 2011:
(1 − 0.348) × (1 + 0.322) × (1 + 0.111) × (1 − 0.014) = 0.652 × 1.322 × 1.111 × 0.986 = 0.9442
Compound total return (cumulative) factor at 5% per year of 5% for five years:
1.055 = 1.2763
,Return needed in 2012 to achieve a compound annualized return of 5%:
1.2763/0.9442 = 1.3517 = 35.2%
Check: 0.944 × 1.352 = 1.276(1/5) = 1.050 = 5% annualized
Consider a portfolio with two assets. Asset A comprises 25% of the portfolio and has a standard
deviation of 17.9%. Asset B comprises 75% of the portfolio and has a standard deviation of 6.2%. If the
correlation of these two investments is 0.5, the portfolio standard deviation is closest to - correct answer
B is correct. The standard deviation of a two-asset portfolio is given by the square root of the portfolio's
variance:
σp=w21σ21+w22σ22+2w1w2ρ1,2σ1σ2⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√
Using this formula, the existing standard deviation is calculated as follows:
0.252×0.1792+0.752×0.0622+2×0.75×0.25×0.5×0.179×0.062⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√=7.90%
Q. An investor with $10,000 decides to borrow an additional $5,000 at the risk-free rate and invest all
the available funds in the market portfolio. This investor's portfolio beta is closest to:
0.5.
1.0.
1.5. - correct answer C is correct. The weight in the market portfolio is 15,000/10,000 = 1.5 and the
weight in the risk-free asset is −5,000/10,000 = −0.5. Because the beta of the risk-free asset is 0 and the
market portfolio's beta is 1, the portfolio's beta is bp = 0(−0.5) + 1(1.5) = 1.5.
Q. The variance of returns of a security and the market portfolio are 0.25 and 0.09, respectively. If the
covariance of security returns and market returns is 0.06, the security's beta is closest to:
0.24.
0.67.
,0.40. - correct answer B is correct. The security's beta is:
βi=Cov(Ri,Rm)σ2m=0.060.09=0.67
Q. The risk-free rate is 5%, and the market risk premium is 8%. If the beta of TRL Corp. is 1.5, based on
the capital asset pricing model (CAPM), the expected return of TRL's stock is closest to:
17.0%.
9.5%.
15.5%. - correct answer A is correct. Using the CAPM relationship of E(Ri) = Rf + [E(Rm) − Rf]bi, we can
estimate the expected return as: E(Ri) = 0.05 + (0.08)(1.5) = 17.0%.
Q. Which of the following performance measures most likely relies on systematic risk as opposed to total
risk when calculating a risk-adjusted return?
Sharpe ratio
M-squared
Treynor ratio - correct answer C is correct. The Treynor ratio measures the return premium of a portfolio
versus the risk-free asset relative to the portfolio's beta, which is a measure of systematic risk.
A is incorrect because the Sharpe ratio is similar to the Treynor ratio, but it uses portfolio standard
deviation, which is a measure of total risk, instead of standard deviation.
B is incorrect because M-squared incorporates the standard deviation of the market and portfolio, which
are measures of total risk.
Q. An analyst uses a multi-factor model to estimate the expected returns of various securities. The model
analyzes historical and cross-sectional return data to identify factors that explain the variance or
covariance in the securities' observed returns. This model is most likely a:
statistical factor model.
macroeconomic factor model.
, fundamental factor model. - correct answer A is correct. Statistical factor models use historical and cross-
sectional return data to identify factors that explain the variance or covariance in the observed returns of
securities.
B is incorrect because macroeconomic factor models use economic factors that are correlated with
security returns, such as economic growth, the interest rate, the inflation rate, productivity, etc.
C is incorrect because fundamental factor models use the relationships between security returns and
firms' underlying fundamentals, such as earnings, earnings growth, cash flow generation, investment in
research, etc.
Q. Based on the capital asset pricing model (CAPM), the expected return on FGL Corp's shares is 12%.
Using a model independent of the CAPM, an analyst has estimated the returns on the stock at 10%.
Based on this information, the analyst is most likely to consider the stock to be:
overvalued.
correctly valued.
undervalued. - correct answer A is correct. Because the estimated return on the stock is lower than the
expected return using the CAPM, the stock does not compensate the investor for the level of risk and so
it is most likely overvalued.
Q. Which of the following institutional investors is most likely to have a low tolerance for investment risk
and relatively high liquidity needs?
Insurance company
Defined-benefit pension plan
Charitable foundation - correct answer A is correct. Insurance companies need to be relatively
conservative and liquid, given the necessity of paying claims when due.
B is incorrect because defined-benefit pension plans tend to have quite high risk tolerances and quite
low liquidity needs.
