Question 1

A stock's beta is more relevant as a measure of risk to an investor who holds only one stock than to an investor who holds a well-diversified portfolio.

Accepted Answer

A stock's beta measures its volatility in relation to the overall market. A beta greater than 1 indicates greater volatility than the market, while a beta less than 1 indicates less volatility than the market.

For an investor who holds only one stock, the stock's beta can be an important measure of risk because it reflects the stock's volatility relative to the market. However, for an investor who holds a well-diversified portfolio, the portfolio's overall beta is less relevant because the portfolio is already diversified and the individual stock's volatility is only one factor among many in determining the portfolio's overall risk. In a well-diversified portfolio, the focus is on reducing unsystematic (company-specific) risk through diversification, rather than relying on any single stock's beta to measure risk.

Question 2

A bond has a $1,000 par value, makes annual interest payments of $100, has 5 years to maturity, cannot be called, and is not expected to default. The bond should sell at a premium if interest rates are below 10% and at a discount if interest rates are greater than 10%.

Accepted Answer

When interest rates are below the coupon rate (in this case, 10%), an investor is willing to pay more for the bond in order to receive the higher fixed interest payments compared to the market rate. Therefore, the bond will sell at a premium. Conversely, when interest rates are above the coupon rate, the bond will sell at a discount.

Question 3

When a loan is amortized, a relatively low percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment's percentage increases in the loan's later years.

Accepted Answer

This is because the interest component of the payment is higher in the early years of the loan, and as the principal reduces over time, the interest component decreases and the principal repayment's percentage increases.

Question 4

The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the greater the percentage of the payment that will be a repayment of principal.

Accepted Answer

This is the basic concept of how an amortized loan works. The payment is structured so that a portion goes towards paying off the interest accrued over the period, while the remaining portion is used to reduce the principal amount owed. As the loan progresses and the principal balance decreases, more of the payment goes towards paying off the principal.

Question 5

Variance is a measure of the variability of returns, and since it involves squaring the deviation of each actual return from the expected return, it is always larger than its square root, its standard deviation.

Accepted Answer

Variance is the average of the squared deviations of each data point from the mean. Taking the square root of variance results in the standard deviation, which measures the dispersion of a dataset. As variance involves squaring the deviation of each actual return from the expected return, it will always be larger than its square root, the standard deviation.

Question 6

All other things held constant, the present value of a given annual annuity decreases as the number of periods per year increases.

Accepted Answer

One could make up an example and see that the statement is true. Alternatively, one could simply recognize that the PV of an annuity declines as the discount rate increases and recognize that more frequent compounding increases the effective rate.

Question 7

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by dividing the periodic rate by the number of periods per year.

Accepted Answer

To find the nominal annual rate from a periodic interest rate, you multiply the periodic rate by the number of periods per year, not divide.

Question 8

You have funds that you want to invest in bonds, and you just noticed in the financial pages of the local newspaper that you can buy a $1,000 par value bond for $800. The coupon rate is 10% (with annual payments), and there are 10 years before the bond will mature and pay off its $1,000 par value. You should buy the bond if your required return on bonds with this risk is 12%.

Accepted Answer

The bonds expected return (YTM) is 13.81%, which exceeds the 12% required return, so buy the bond.

Question 9

If the returns of two firms are negatively correlated, then one of them must have a negative beta.

Accepted Answer

The answer of If the returns of two firms are...

Question 10

Portfolio A has but one stock, while Portfolio B consists of all stocks that trade in the market, each held in proportion to its market value. Because of its diversification, Portfolio B will by definition be riskless.

Accepted Answer

While Portfolio B may be less risky than Portfolio A due to diversification, it cannot be completely riskless as the overall market can still experience fluctuations and volatility.

Question 11

Portfolio A has but one security, while Portfolio B has 100 securities. Because of diversification effects, we would expect Portfolio B to have the lower risk. However, it is possible for Portfolio A to be less risky.

Accepted Answer

It is possible for Portfolio A to hold the least risky security, which would make it less risky than Portfolio B even though Portfolio B has more diversification. However, as a general rule, diversification lowers risk.

Question 12

It is possible for a firm to have a positive beta, even if the correlation between its returns and those of another firm is negative.

Accepted Answer

Beta measures the relationship between the returns of a stock and the overall market. A positive beta indicates that the stock tends to move in the same direction as the market, while a negative beta indicates that the stock tends to move in the opposite direction. The correlation between two stocks measures the strength and direction of their relationship, but does not necessarily determine the beta of either stock. Therefore, it is possible for a firm to have a positive beta even if the correlation between its returns and those of another firm is negative.

Question 13

The present value of a future sum decreases as either the discount rate or the number of periods per year increases, other things held constant.

Accepted Answer

This is true according to the time value of money principle. When the discount rate or the number of periods per year increases, the present value of a future sum decreases because the money is worth less in the future.

Question 14

Because of differences in the expected returns on different investments, the standard deviation is not always an adequate measure of risk. However, the coefficient of variation adjusts for differences in expected returns and thus allows investors to make better comparisons of investments' stand-alone risk.

Accepted Answer

This statement is true. The coefficient of variation takes into account the expected return of investments, which allows for better comparisons of risk. Standard deviation alone may not accurately represent risk when comparing investments with different expected returns.

Question 15

As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or less than the nominal rate on the deposit (or loan).

Accepted Answer

The effective annual rate (EAR) takes into account the compounding effect within a year, and as a result, it is often higher than the nominal rate (or stated rate) which does not account for compounding.

Question 16

A stock's beta measures its diversifiable risk relative to the diversifiable risks of other firms.

Accepted Answer

A stock's beta measures its systematic risk, or the risk that cannot be diversified away by investing in a portfolio of stocks. Beta compares the stock's volatility to that of the market as a whole, not to the diversifiable risk of other firms.

Question 17

The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the greater the present value of a given lump sum to be received at some future date.

Accepted Answer

The greater number of compounding periods increases the future value of a lump sum investment due to more frequent application of interest, but it decreases the present value of a future lump sum because more compounding periods mean a higher effective discount rate is applied, reducing the present value.

Question 18

The prices of high-coupon bonds tend to be less sensitive to a given change in interest rates than low-coupon bonds, other things held constant.

Accepted Answer

The reason for this is that more of the cash flows of a low-coupon bond comes late in the bond's life (as the maturity payment), and later cash flows are impacted most heavily by changing market rates.

Question 19

A portfolio's risk is measured by the weighted average of the standard deviations of the securities in the portfolio. It is this aspect of portfolios that allows investors to combine stocks and thus reduce the riskiness of their portfolios.

Accepted Answer

The risk of a portfolio is not just the weighted average of the standard deviations of the securities, but also takes into account the correlation between the securities. Combining stocks does not always reduce the riskiness of a portfolio, as some stocks may move in unison and increase the overall risk. Diversification, by combining stocks with low or negative correlations, can reduce the overall risk of the portfolio.

Question 20

Suppose Randy Jones plans to invest $1,000. He can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be somewhat less than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)

Accepted Answer

Work out the numbers with a calculator:
 $\begin{array} { l c c } 
\text { PV } & 1000 \mathrm { FV } = & \$ 1,710.34 \
\text { Rate on A } & 5 \% 2 \times \mathrm { FV } _ { \mathrm { A } } = & \$ 3,420.68 \
\text { Rate on B } & 12 \% FV _ { \mathrm { B } } = & \$ 3,478.55 \
\text { Years } & 11 \mathrm { FV } _ { \mathrm { B } } > 2 \times \mathrm { FV } _ { \mathrm { A } } so \mathrm {   \textrm {FAL } \mathrm { SE } } &
\end{array}$

Quiz 29: Basic Financial Tools: A review