Reading 62: portfolio risk and return- part I Flashcards
An investor buys a share of stock for $40 at time t = 0, buys another share of the same stock for $50 at t = 1, and sells both shares for $60 each at t = 2. The stock paid a dividend of $1 per share at t = 1 and at t = 2. The periodic money-weighted rate of return on the investment is closest to:
22.2%.
23.0%.
23.8%.
Using the cash flow functions on your financial calculator, enter CF0 = –40; CF1 = –50 + 1 = –49; CF2 = 60 × 2 + 2 = 122; CPT IRR = 23.82%. (LOS 62.a)
Which of the following asset classes has historically had the highest returns and standard deviation of returns?
Small-cap stocks.
Large-cap stocks.
Long-term corporate bonds.
Small-cap stocks have had the highest annual return and standard deviation of return over time. Large-cap stocks and bonds have historically had lower risk and return than small-cap stocks. (LOS 62.c)
Which of the following statements about risk-averse investors is most accurate? A risk-averse investor:
seeks out the investment with minimum risk, while return is not a major consideration.
will take additional investment risk if sufficiently compensated for this risk.
avoids participating in global equity markets.
Risk-averse investors are generally willing to invest in risky investments, if the expected return of the investment is sufficient to reward the investor for taking on this risk. Participants in securities markets are generally assumed to be risk-averse investors. (LOS 62.d)
The capital allocation line is a line from the risk-free return through:
the global maximum-return portfolio.
the optimal risky portfolio.
the global minimum-variance portfolio.
An investor’s optimal portfolio will lie somewhere on the capital allocation line, which begins at the risk-free asset and runs through the optimal risky portfolio. (LOS 62.e)
In a 5-year period, the annual returns on an investment are 5%, -3%, -4%, 2%, and 6%. The standard deviation of annual returns on this investment is closest to:
4.0%.
4.5%.
20.7%.
mean annual return = (5% – 3% – 4% + 2% + 6%) / 5 = 1.2%
Squared deviations from the mean:
sum of squared deviations = 14.44 + 17.64 + 27.04 + 0.64 + 23.04 = 82.8
sample variance = 82.8 / (5 – 1) = 20.7
sample standard deviation = 20.71/2 = 4.55%
(LOS 62.f)
A measure of how the returns of two risky assets move in relation to each other is:
the range.
the covariance.
the standard deviation.
The covariance is defined as the co-movement of the returns of two assets or how well the returns of two risky assets move together. Range and standard deviation are measures of dispersion and measure risk, not how assets move together. (LOS 62.f)
Which of the following statements about correlation is least accurate?
Diversification reduces risk when correlation is less than +1.
If the correlation coefficient is 0, a zero-variance portfolio can be constructed.
The lower the correlation coefficient, the greater the potential benefits from diversification.
A zero-variance portfolio can only be constructed if the correlation coefficient between assets is –1. Diversification benefits can be had when correlation is less than +1, and the lower the correlation, the greater the expected benefit. (LOS 62.f)
The variance of returns is 0.09 for Stock A and 0.04 for Stock B. The covariance between the returns of A and B is 0.006. The correlation of returns between A and B is:
0.10.
0.20.
0.30.
RootA = v/0.09 = 0.30
RootBv/0.04 = 0.20
correlaion= 0.006 / [(0.30)(0.20)]= 0.10
A portfolio was created by investing 25% of the funds in Asset A (standard deviation = 15%) and the balance of the funds in Asset B (standard deviation = 10%).
If the correlation coefficient is 0.75, what is the portfolio’s standard deviation?
10.6%.
12.4%.
15.0%.
Root(0.25)^2(0.15)^2+(0.75)^2(0.10)^2+2(0.25)(0.75)(0.15)(0.10)(0.75)=
Root0.001406+0.005625+0.004219 = Root0.01125= 0.106
A portfolio was created by investing 25% of the funds in Asset A (standard deviation = 15%) and the balance of the funds in Asset B (standard deviation = 10%).
If the correlation coefficient is -0.75, what is the portfolio’s standard deviation?
2.8%.
4.2%.
5.3%.
Root(0.25)^2(0.15)^2+(0.75)^2(0.10)^2+2(0.25)(0.75)(0.15)(0.10)(-0.75)=
Root0.001406+0.005625-0.004219 = Root0.002812= 0.053
Which of the following statements about covariance and correlation is least accurate?
A zero covariance implies there is no linear relationship between the returns on two assets.
If two assets have perfect negative correlation, the variance of returns for a portfolio that consists of these two assets will equal zero.
The covariance of a 2-stock portfolio is equal to the correlation coefficient times the standard deviation of one stock’s returns times the standard deviation of the other stock’s returns.
If the correlation of returns between the two assets is –1, the set of possible portfolio risk/return combinations becomes two straight lines (see Figure 62.2). A portfolio of these two assets will have a positive returns variance unless the portfolio weights are those that minimize the portfolio variance. Covariance is equal to the correlation coefficient multiplied by the product of the standard deviations of the returns of the two stocks in a 2-stock portfolio. If covariance is zero, then correlation is also zero, which implies that there is no linear relationship between the two stocks’ returns. (LOS 62.h)
