62 - Portfolio Risk and Return Part 1

Question 1

As the correlation between the returns of two assets becomes lower, the risk reduction potential becomes:

Answer 1

Perfect positive correlation (r = +1) of the returns of two assets offers no risk reduction, whereas perfect negative correlation (r = -1) offers the greatest risk reduction.

(Module 62.4, LOS 62.h)

Question 2

There are benefits to diversification as long as:

Answer 2

There are benefits to diversification as long as the correlation coefficient between the assets is less than 1.

(Module 62.4, LOS 62.h)

Question 3

An analyst gathered the following data for Stock A and Stock B:

Time Period Stock A Returns Stock B Returns
1 10% 15%
2 6% 9%
3 8% 12%
What is the covariance for this portfolio?

Answer 3

The formula for the covariance for historical data is:

cov1,2 = {Σ[(Rstock A − Mean RA)(Rstock B − Mean RB)]} / (n − 1)

Mean RA = (10 + 6 + 8) / 3 = 8, Mean RB = (15 + 9 + 12) / 3 = 12

Here, cov1,2 = [(10 − 8)(15 − 12) + (6 − 8)(9 − 12) + (8 − 8)(12 − 12)] / 2 = 6

(Module 62.3, LOS 62.f)

Question 4

An investor begins with a $100,000 portfolio. At the end of the first period, it generates $5,000 of income, which he does not reinvest. At the end of the second period, he contributes $25,000 to the portfolio. At the end of the third period, the portfolio is valued at $123,000. The portfolio’s money-weighted return per period is closest to:

Answer 4

Using the financial calculator, the initial investment (CF0) is –100,000. The income is +5,000 (CF1), and the contribution is –25,000 (CF2). Finally, the ending value is +123,000 (CF3) available to the investor. Compute IRR = 0.94

(Module 62.1, LOS 62.a)

Question 5

If two stocks have positive covariance:

Answer 5

For two stocks with positive covariance, their prices will tend to move together over time and they will tend to produce rates of return greater than their mean returns at the same time and produce rates of return less than their mean returns at the same time.

Positive covariance does not necessarily imply strong positive correlation. Two stocks need not be in the same industry to have a positive covariance.

(Module 62.3, LOS 62.f)

Question 6

An investor buys one share of stock for $100. At the end of year one she buys three more shares at $89 per share. At the end of year two she sells all four shares for $98 each. The stock paid a dividend of $1.00 per share at the end of year one and year two. What is the investor’s money-weighted rate of return?

Answer 6

T = 0: Purchase of first share = -$100.00

T = 1: Dividend from first share = +$1.00

Purchase of 3 more shares = -$267.00

T = 2: Dividend from four shares = +4.00

Proceeds from selling shares = +$392.00

The money-weighted return is the rate that solves the equation:

$100.00 = -$266.00 / (1 + r) + 396.00 / (1 + r)2.

CFO = -100; CF1 = -266; CF2 = 396; CPT → IRR = 6.35%.

Question 7

Becky Scott and Sid Fiona have the same expectations about the risk and return of the market portfolio; however, Scott selects a portfolio with 30% T-bills and 70% invested in the market portfolio, while Fiona holds a leveraged portfolio, having borrowed to invest 130% of his portfolio equity value in the market portfolio. Regarding their preferences between risk and return and their indifference curves, it is most likely that:

Answer 7

Even risk-averse investors will prefer leveraged risky portfolios if the increase in expected return is enough to offset the increase in portfolio risk. Scott’s portfolio selection implies that she is more risk averse than Fiona, has steeper indifference curves, and is willing to take on less additional risk for an incremental increase in expected returns than Fiona.

(Module 62.4, LOS 62.e)

Question 8

Which of the following is most accurate with respect to the relationship of the money-weighted return to the time-weighted return? If funds are contributed to a portfolio just prior to a period of favorable performance, the:

Answer 8

A: money-weighted rate of return will tend to be elevated.

The time-weighted returns are what they are and will not be affected by cash inflows or outflows. The money-weighted return is susceptible to distortions resulting from cash inflows and outflows. The money-weighted return will be biased upward if the funds are invested just prior to a period of favorable performance and will be biased downward if funds are invested just prior to a period of relatively unfavorable performance. The opposite will be true for cash outflows.

Question 9

Smith has more steeply sloped risk-return indifference curves than Jones. Assuming these investors have the same expectations, which of the following best describes their risk preferences and the characteristics of their optimal portfolios? Smith is:

Answer 9

Steeply sloped risk-return indifference curves indicate that a greater increase in expected return is required as compensation for assuming an additional unit of risk, compared to less-steep indifference curves. The more risk-averse Smith will choose an optimal portfolio with lower risk and a lower expected return than the less risk-averse Jones’s optimal portfolio.

(Module 62.4, LOS 62.e)

Question 10

Which of the following statements regarding the covariance of rates of return is least accurate?

Answer 10

If the covariance is negative, the rates of return on two investments will always move in different directions relative to their means.

Negative covariance means rates of return for one security will tend to be above its mean return in periods when the other is below its mean return, and vice versa. Positive covariance means that returns on both securities will tend to be above (or below) their mean returns in the same time periods. For the returns to always move in opposite directions, they would have to be perfectly negatively correlated. Negative covariance by itself does not imply anything about the strength of the negative correlation, it must be standardized by dividing by the product of the securities’ standard deviations of return.

(Module 62.3, LOS 62.f)