Unit 4: Risk and Return

T or F: Low standard deviation stocks always have low betas

FALSE

T or F: One can easily calculate the estimated risk premium on stocks via the statistical analysis of historical stock returns.

FALSE

T or F: The variability of a well-diversified portfolio mostly reflects the contribnutions to risk from the standard deviations of the stocks within that portfolio

FALSE

T or F: Treasury bills typically provide higher average returns, both in nominal terms and in real terms, than long-term government bonds.

FALSE

The portfolio risk that cannot be eliminated by diversification is called unique risk.

FALSE

T or F: If returns on two stocks tended to move in opposite directions, then the covariances and correlations on the two stocks would be negative.

TRUE

T or F: The beta of a well-diversified portfolio is equal to the value weighted average beta of the securities included in the portfolio.

TRUE

The Beta of the market portfolio is:

+1.0

What range of values can correlation coefficients take?

-1 to +1

For a two-stock portfolio, the maximum reduction in risk occurs when the correlation coefficient between the two stocks equals:

-1.0

How can individual investors diversify?

A very simple way for an individual investor to diversify is to buy shares in a mutual fund that holds a diversified portfolio.

What is the correct measure of the opportunity cost of capital regardless of the timing of cash flows?

Arithmetic Average

Discuss the importance of beta as a measure of risk.

Beta is a measure of market risk. It is also called the relative measure of risk as it measures risk relative to the market portfolio. Beta is useful as a measure of risk in the context of well-diversified portfolios. It measures the risk contribution of a single security to the portfolio.

Explain why international stocks may have high standard deviations but low betas.

Beta is traditionally measured relative to the S&P 500 index. As such, there may be a weaker statistical relationship between the S&P 500 and an international stock. If these two assets are mostly independent of one another, there is little change they will have a statistically significant covariance. With a low covariance, by definition, the stock will have a low beta. This could occur even if the standard deviation of the beta is very high. This answer assumes that the market risk in domestic stocks is largely independent of the market risk in international stocks.

A statistical measure of the degree to which securities' returns move together is called

Correlation coefficient

Briefly explain how diversification reduces risk

Diversification reduces risk because prices of different securities do not move exactly together. When you form portfolios using a large number of stocks, the variability of the portfolio is much less than the average variability of individual stocsk.

For log normally distributed returns, the annual geometric average return is greater than the arithmetic average return

FALSE

T or F: A portfolio with a beta of one offers an expected return equal to the market risk premium

FALSE

T or F: By purchasing U.S. government bonds, an investor can achieve both a risk-free nominal rate of return and a risk-free real rate of return.

FALSE

The standard statistical measures of the variability of stock returns are beta and covariance

FALSE

Briefly explain what the beta of a stock means.

For each additional 1% change in the market return, the return on the stock on average changes by beta times 1%. For example, if the beta of IBM is 1.59, then for an additional 1% change in the market return, the expected change in the return of IBM stock will equal 1.59%.

Briefly explain the concept of value additivity

If the capital market establishes a value PV(A) for asset A and PV(B) for asset B, the market value of a firm that holds both these assets is given by: PV(AB) = PV(A) + PV(B). This logic can be extended for any number of assets. Value additivity is also applicable to cash flows. We can add the present values of two separate cash flows and get the present value of the combined cash flows. It can be stated as follows: PV(A+B) = PV(A) + PV(B) and PV(A+B+C) = PV(A) +PV(B) + PV(C) This idea can be extended for any number of cash flows.

In the formula for calculating the variance of an N-stock portfolio, how many covariance and variance terms are there?

In the formula for calculating the variance of an N-stock portfolio, there are [N(N-1)]/2 different covariance terms and N variance terms.

For long-term U.S. government bonds, which risk concerns investors the most?

Interest rate risk

For a portfolio of N-stocks, the formula for portfolio variance contains

N(N-1)/2 different covariance terms

Briefly explain how the beta of a stock is estimated.

One can estimate the beta of a stock by plotting the market returns on the x-axis and the corresponding stock returns on the y-axis. The slope of the resulting line of best fit is the beta estimate for the stock. Beta = Cov(Stock A, Market) / Var (M)

T or F: The covariance between the returns on two stocks equals the correlation coefficient multiplied by the standard deviations of the two stocks.

TRUE

The beta of a well-diversified portfolio is equal to the value weighted average beta of the securities included in the portfolio

TRUE

What is the beta of a portfolio with a large number of randomly selected stocks?

The beta of a portfolio with a large number of randomly selected stocks equals one. The standard deviation of such a portfolio is equal to the standard deviation of the market.

Define the term risk premium

The difference between the security return and the risk-free rate, such as a Treasury bill return, is called the risk premium. This denotes the additional return on the security because of additional risk.

Briefly explain how individual securities affect portfolio risk.

The risk of a well-diversified portfolio depends on the market risk of the securities included in the portfolio. Portfolio beta is the weighted average of individual security betas included in the portfolio. Individual securities affect portfolio risk to the extent that they change the beta of the portfolio.

What is an estimate of standard error?

The standard deviation of returns divided by the square root of the number of observations.

Regarding stock returns, briefly explain the term variance.

Variance is a standard statistical measure of spread. The variance is the expected squared deviation from the expected return. From a finance point of view, this measures the total risk of a portfolio: the higher the variance, the higher the risk of the portfolio. This is also called a measure of total risk.

Briefly explain the difference between beta as a measure of risk and variance as a measure of risk.

Variance measures the total risk of a security and is a measure of stand-alone risk. Total risk has both unique risk and market risk. In a well-diversified portfolio, unique risks tend to cancel each other out and only market risk remains. Beta is a measure of market risk and is useful in the context of a well-diversified portfolio. Beta measures the sensitivity of the security returns to changes in market returns. The market portfolio has a beta of one and thus has average risk.

Unique risk is also called

firm-specific risk