C15 - Portfolio Management (25-30 Qs C15-C17) BC Flashcards
According to CAPM, if the risk-free rate of return is 3%, the expected return to the market is 11%, what is the expected return to a portfolio with a beta of 0?
A) 0.0%
B) 3.0%
C) 5.0%
D) 11.0%
Capital asset pricing model (CAPM)
B - 3%
Expected return on the portfolio (CAPM) = Rf + βp (E(Rm)-Rf)
E(Rp) = 3 + 0(11-3) = 3%
The pieces of the CAPM formula are the risk-free rate (Rrf), investment beta (βa) and the market return (Rm – Rrf). The value of each piece is dynamic, so the CAPM calculation needs to be updated over time. The formula is represented symbolically as: Ra = Rrf + [βa * (Rm – Rrf)], with Ra being the expected return.
β = 0 means no market sensitivity, uncorrelated with the market
β < 1 means Low market sensitivity, less volatile than the market
β = 1 means same as market, neutral
β > 1 means high market sensitivity, more volatile than the market
β < 0 means negative market sensitivity, moves in the opposite direction of the market
When there is an increase in the number of assets in a portfolio, total risk is reduced due to the:
A) Increase in unsystematic risk
B) Increase in systemeatic risk
C) Decrease in unsystematic risk
D) Decrease in systematic risk
C - Decrease in unsystematic risk
- Systematic risk refers to the risk inherent to the entire market. Systematic risk, also known as undiversifiable risk, volatility risk, or market risk, affects the overall market, not just a particular stock or industry.
- Unsystematic risk refers to risks that are not shared with a wider market or industry. Unsystematic risks are often specific to an individual company, due to their management, financial obligations, or location. Unlike systematic risks, unsystematic risks can be reduced by diversifying one’s investments.
If the expected return on a share is 17.6%, the market expected return is 20% and the risk-free return is 8%, what is the share’s beta?
A) 0
B) 1
C) 0.8
D) 1.2
C - 0.8
Use CAPM formula and rearrange to solve for Beta.
17.6% = 8% + ? (20% - 8%)
Rearrange:
17.6% - 8% = ? (12%)
9.6% = ? (12%)
? = 9.6% / 12%
? = 0.8
CAPM Formula: Ra = Rrf + [βa * (Rm – Rrf)] with:
* risk-free rate (Rrf)
* investment beta (βa)
* market return (Rm – Rrf)
* Ra being the expected return.
CAPM - Capital asset pricing model
What is the expected return on a security with a beta of 1.5 if the market risk premium is 6% and the risk-free return is 4%?
A) 6%
B) 7%
C) 9%
D) 13%
D - 13%
CAPM Formula: Ra = Rrf + [βa * (Rm – Rrf)] with:
* (Rrf) risk-free rate
* (Rm) average expected rate of return on the market
* (βa) investment beta
* (Rm – Rrf) market return
* (Ra) being the expected return.
The market risk premium IS “(Rm - Rf)” SO
Expected Return = 0.04 + (1.5 * (0.06)) = 0.13 i.e. 13%
CAPM - Capital asset pricing model
What measure of risk is used in the security market line?
A) Standard deviation
B) Beta
C) Default
D) Variance
B - Beta (β)
Beta is a statistical measure that compares the volatility of a particular stock’s price movements to the overall market. In simple terms, it indicates how much the price of a specific security will move in relation to market movements.
- β = 0 means no market sensitivity, uncorrelated with the market
- β < 1 means Low market sensitivity, less volatile than the market
- β = 1 means same as market, neutral
- β > 1 means high market sensitivity, more volatile than the market
- β < 0 means negative market sensitivity, moves in the opposite direction of the market
A stock has a beta of 0.8; the risk-free return is 9%, if the market return was 15%, what would the expected return of the stock be?
A) 12%
B) 13.2%
C) 13.8%
D) 14.2%
C - 13.8%
CAPM Formula: Ra = Rrf + [βa * (Rm – Rrf)] with:
* (Rrf) risk-free rate
* (Rm) average expected rate of return on the market
* (βa) investment beta
* (Rm – Rrf) market return
* (Ra) being the expected return.
Expected Return = 0.09 + (0.8 * (0.15 - 0.09)) = 0.138 i.e. 13.8%
Which of the following is NOT an assumption of the Capital Asset Pricing Model?
A) No taxes
B) All investors agree on the same investment period
C) Investors can borrow or lend at the same risk-free rate
D) Financial markets are monopolistic
D - Financial markets are monopolistic
If the beta of portfolio = 0.72 and the covariance of the portfolio with the same return on the market is 273. What is the variance?
A) 379.17
B) 124.56
C) 201
D) 196.56
A - 379.17
Beta = Cov(Portfolio, Market) / Variance Market
Solve for variance 273 / 0.72 = 379.17
The standard deviation of a well diversified portfolio is equal to:
A) CAPM Beta
B) the standard deviation of the market
C) the square of the CAPM beta
D) the specific risk of the individual securities invested in the fund
B - the standard deviation of the market
The return to a portfolio covaries exactly with the return of the market, if the:
A) Beta of the portfolio is -1
B) expected returns for both are the same
C) return on the market is lower
D) return on the market is higher
B - expected returns for both are the same
β = 1 means same as market, neutral
Which of the following are TRUE of systematic risk?
1. It can be controlled by diversification
2. It is the total risk for a fully diversified portfolio
3. It is the risk particular to a particular investment
A) 1 and 3
B) 2 and 3
C) 2 only
D) 1 only
C - 2 (It is the total risk for a fully diversified portfolio) only
Systematic risk refers to the risk inherent to the entire market. Systematic risk, also known as undiversifiable risk, volatility risk, or market risk, affects the overall market, not just a particular stock or industry. It cannot be controlled, but it can be the total risk if a portfolio is fully diversified so that risk for specific investments are balanced out to be neutral overall.
If the CAPM beta = 0.8 and the variance of the market is 200, what is the covariance of the portfolio with the market?
A) 250
B) 1600
C) 80
D) 160
D - 160
Beta = Cov(Portfolio, Market)/ Variance Market
0.8 = ? / 200
Rearrange
? = 0.8 x 200 = 160
CAPM - Capital Asset Pricing Model
Security X has a beta of 0.7. Security Y has a beta of 1.3. An investor has £100 and wishes to generate returns consistent with a beta of 1 Which of the following weightings should he adopt?
A) X = 80% / Y = 20%
B) X = 70% / Y = 30%
C) X = 30% / Y = 70%
D) X = 50% / Y = 50%
D - 50/50
(50% x 0.7) + (50% x 1.3) = 1
What can be associated with a security that has a beta less than one?
A) Yields generally LOWER returns than a security with a beta of more than one
B) Yield generally HIGHER returns than a security with a beta of more than one
C) Systematic risk is greater if the beta is less than one
D) The unsystematic risk is the same in both securities
A - Yields generally LOWER returns than a security with a beta of more than one
A Beta of less than 1 implies a risk lower than the market and hence a lower return
- β = 0 means no market sensitivity, uncorrelated with the market
- β < 1 means Low market sensitivity, less volatile than the market
- β = 1 means same as market, neutral
- β > 1 means high market sensitivity, more volatile than the market
- β < 0 means negative market sensitivity, moves in the opposite direction of the market
An active management strategy assumes better results can be obtained by taking on:
A) Idiosyncratic risk
B) Market risk
C) Systematic risk
D) All of the above
A - Idiosyncratic risk
- Idiosyncratic risk is the risk of loss that’s specific to a particular investment, like a stock or sector. It’s also known as unsystematic risk.
- Market risk is the risk that arises from movements in stock prices, interest rates, exchange rates, and commodity prices.
- Systematic risk refers to the risk inherent to the entire market. Systematic risk, also known as undiversifiable risk, volatility risk, or market risk, affects the overall market, not just a particular stock or industry.
If the total risk of a fund equals 576 (in variance terms), and specific risk is 14% What is systematic risk?
A) 380
B) 100
C) 19.49%
D) 10%
C - 19.49%
Total risk = Specific Risk + Systematic risk (in variance terms)
576 = 14^2 + Systematic risk^2
576 - 196 = Systematic risk^2
Systematic risk^2 = 380
Systematic risk in standard deviation terms = Square root of 380 = 19.49%
Share Z has a beta of 0.75. Share A has a beta of 1.25. An investor has £100 and wishes to generate returns consistent with a beta of 1
How much of the £100 should go into each share?
A) Z: £90 / A: £10
B) Z: £10 / A: £90
C) Z: £75 / A: £25
D) Z: £50 / A: £50
D - Z: £50 / A: £50
We need a weighted average beta of 1. SO:
(0.5 x 0.75) + (0.5 x 1.25) = 1
A portfolio is madeup of two shares X and Y, with betas of 0.7 and 1.1 respectively 70% of your money is invested in X, and the rest in Y, what is the beta of your portfolio?
A) 0.82
B) 0.78
C) 0.95
D) 1.26
A - 0.82
(0.7 x 0.7) + (0.3 x 1.1) = 0.82
Using the following details about two portfolios, which of the following statements is TRUE?
Portfolio A: Correlation coefficient with the market +0.94
Portfolio B: Correlation coefficient with the market +0.62
A) Portfolios A and B are well diversified
B) Portfolkio A and B are poorly diversified
C) Portfolio A is well diversified, portfolio B is relatively diversified
D) Portfolio B is well diversified, portfolio A is relatively poorl diversified
C - Portfolio A is well diversified, portfolio B is relatively diversified
If a portfolio is well diversified, you would expect a strong correlation to the market. The closer to +1, the stronger the correlation and therefore the better diversified.
Using the Capital Asset Pricing Model, what is the market risk premium given the following:
Beta of Share A: 0.75
Risk free rate of return: 5%
Expected return on the market: 12%
A) 5.25%
B) 7%
C) 10.25%
D) 9%
B - 7%
Market risk premium = market return - Risk-free rate
SO 12% - 5% = 7%
Which of the following is the CORRECT equation for the beta of share J?
A) The covariance of share J and the market divided by the variance of the market
B) The covariance of share J and the market divided by the variance of share J
C) The covariance of share J and market divided by the standard deviation of the market
D) The covariance of share J and the market divided by the standard deviation of share J
A - The covariance of share J and the market divided by the variance of the market
Covariance is a statistical measurement that shows how the returns of two assets move in relation to each other. It’s used in investment management to help investors understand how assets perform relative to each other, and to diversify their portfolios.
If the covariance between a share and the market is 5 and the standard deviation of the market equals 2, what is the share’s beta?
A) 1.10
B) 1.25
C) 2.25
D) 2.50
B - 1.25
Beta = Covariance / Market Variance SO
Beta = 5 / 2^2 = 1.25
A portfolio is made up of two shares M and N with betas of 0.2 and 1.2 respectively 50% of your money is invested in M, the rest in N, what is the beta of your portfolio?
A) 0.6
B) 0.7
C) 0.8
D) 1.0
B - 0.7
Portfolio Beta = (allocation M x Beta M) + (Allocation N x Beta N) SO
(0.5 x 0.2) + (0.5 x 1.2) = 0.7
If the market return is 11% and the risk-free rate is 3%, whar is the market-risk premium?
A) 14%
B) 11%
C) 3%
D) 8%
D - 8%
Market risk premium = Market Return - Risk-free rate SO:
11% - 3% = 8%