UNIT #23: Portfolio Performance Measures

A stock is currently worth $75. If the stock was purchased one year ago for $60, and the stock paid a $1.50 dividend over the course of the year, what is the holding period return? A) 22.0% B) 27.5% C) 24.0% D) 25.0%

B *(75 − 60 + 1.50) ÷ 60 = 0.2750, or 27.5%.

In order to compute yield to maturity, all of the following are necessary EXCEPT A) the nominal yield B) the call price C) the current market price D) the maturity date

B *Computing the yield to maturity (YTM) does not require the call price or call date—that is necessary to compute the yield to call (YTC). We do need to know the current market price, the coupon (nominal yield) and the maturity date.

GHI common stock has a $10 par value and is selling in the market for $60 per share. If the current quarterly dividend is $1, the current yield is A) 1% B) 6.7% C) 10% D) 1.7%

B *Current yield is determined by dividing the annual dividend of $4 ($1 per quarter × 4 = $4) by the current stock price of $60 ($4 ÷ $60 = 6.7%). The par value of the common stock has no relevance to this question.

An investor purchased stock for $50 per share at the beginning of the year. In December, the investor liquidated his stock for $55 per share, while also receiving dividends of $2 per share during the year. Assuming an inflation rate of 3%, what is the investor's real rate of return? A) 4% B) 11% C) 10% D) 14%

B *Given the fact the client liquidated his shares at a price of $55, we can conclude that he attained a 10% ($5 profit ÷ $50 initial investment) return based on capital appreciation of the stock. He also received dividends of $2 per share giving him an additional return of 4% ($2 ÷ $50). By adding these 2 percentages together, we can conclude that his total return is 14%, less an inflation rate of 3%, which would give a real rate of return of 11%.

An investment advisory firm tracks its performance against the S&P 400. From this, you could determine that this firm concentrates on A) Nasdaq securities B) large-cap securities C) small-cap securities D) mid-cap securities

D *The S&P 400 is known as the mid-cap index.

This is the performance of your portfolio over the previous 4 years: -Year 1 - 10% -Year 2 - 45% -Year 3 + 20% -Year 4 + 35% In order for the portfolio to be equal to the starting investment, the return in Year 5 must be nearest to A) 33%. B) 25%. C) 0%. D) 20%.

* -In Year 1, you lose 10%. Your portfolio is now worth $1,000 x (1 - 0.1) = $1,000 x 0.9 = $900. -In Year 2, you lose 45%. Your portfolio is now worth $900 x (1 - 0.45) = $900 x 0.55 = $495. -In Year 3, you gain 20%. Your portfolio is now worth $495 x (1 + 0.2) = $495 x 1.2 = $594. -In Year 4, you gain 35%. Your portfolio is now worth $594 x (1 + 0.35) = $594 x 1.35 = $801.9. -You would like to know by how much your portfolio needs to appreciate in Year 5 to be worth its original value of $1,000. Let's set "y" to be this number. Then we have: -$801.9 x (1 + y) = $1,000. Solving this equation for "y" gives: y = ($1,000 ÷ $801.9) - 1 = 0.247 = 24.7%. Rounding this answer in percentage terms (24.7%) to the nearest integer yields the desired answer of 25%. -Your portfolio thus needs to increase by nearly 25% in Year 5 for it to be worth its original value of $1,000. -Some might find it easier to look at the shortfall ($1,000 - $801.90) = $198.10. Divide that by the current value and you have 198.10 ÷ 801.90 = 24.7%. -Some might just look at the number and recognize that you are about $200 short on a value of $800 and that is 25%.

An investor buys 100 shares of KAPCO stock for $120 per share. During the year, he receives $260 in dividends and, at the end of the year, the stock is worth $13,000. The investor's holding period return is A) 10.50% B) 8.33% C) 2.17% D) 9.69%

A *Holding period return is computed by dividing the total return from income (dividends or interest) plus appreciation (or minus depreciation), by the original cost. In this example, the investor received $260 in income and has $1,000 of appreciation. That is a total return of $1,260 divided by $12,000 or 10.50%

In the formula for determining the real rate of return, A) the inflation rate is subtracted from the investment return B) the investment return is divided by the inflation rate C) the marginal tax bracket is subtracted from the investment return D) the inflation rate is divided by the investment return

A *In computing the real rate of return, which represents inflation-adjusted compounding (or discounting), a formula is applied in which the rate of inflation (usually as measured by the CPI) is subtracted from the investor's rate of return.

Your firm's market analyst believes the current bullish market in equities will continue. Your moderately conservative clients should consider investing in an ETF or index fund tracking the A) S&P 500 B) Dow Jones 15 utilities C) Russell 2000 D) MSCI EAFE

A *The S&P 500 represents the largest companies and, as a result, is most suitable for a growth-oriented investor with a moderate risk tolerance. The Russell 2000 is the small-cap benchmark and carries more than a moderate level of risk as does the MSCI EAFE index which is composed of foreign securities. Utilities are for those who are more than moderately conservative. Furthermore, utilities, being defensive issues, are likely to participate in a bullish market to a very small degree.

Which of the following quantitative tools is used to measure risk-adjusted returns? A) Sharpe ratio B) Standard deviation C) Correlation D) Beta

A *The Sharpe ratio is used to measure risk-adjusted returns. Beta does enable one to evaluate the potential market risk, but, strictly speaking, does not measure risk-adjusted return. Correlation measures the movement of one security in relationship to the movement of another. Standard deviation measures the volatility of a security, not its risk-adjusted returns. Standard deviation has input in the Sharpe ratio but it is the ratio itself that measures risk-adjusted returns.

If you knew a given stock had a 40% chance of earning a 10% return, a 40% chance of earning −20%, and a 20% chance of earning −10%, the expected return would be equal to A) −6% B) 10% C) −10% D) 14%

A *The expected return is computed by taking the probability of each possible return outcome, multiplying it by the return outcome itself, and then adding them all together. In this case, the math is as follows: (0.4 × 10%) + (0.4 × −20%) + (0.2 × −10%), or +4% − 8% − 2%, which equals -6%. Part of the trick here is catching the probable negative returns and the ridiculous assumption that an investor would consider looking at a stock with this kind of expected return. You can always count on NASAA to surprise you.

If the return on Treasury bills is 3% and the equity risk premium is 4%, the expected equity returns should be A) 7% B) 1% C) 12% D) 4%

A *The expected return on an equity investment is the risk-free (for example, T-bill) rate of return added to the equity risk premium (3% + 4% = 7%).

Using the following information, compute the inflation-adjusted rate of return for an investor holding the ABC Corporation's 20-year bond: -Coupon rate 5%, paid semi-annually -Rating Aa -Maturity date December 1, 2046 -CPI 2% -Par value $1,000 -Purchase price 90 -Call date December 1, 2033 -Call price 101 A) 3.56% B) 4.50% C) 5.00% D) 2.50%

A *The inflation-adjusted rate of return is the actual return (income received divided by the purchase price) less the inflation rate as measured by the CPI. In this example, the bond pays $50 per year on an investment of $900. That is an actual return of 5.56%. Subtracting the CPI of 2% gives us an inflation-adjusted, or real, rate of return of 3.56%.

An investment is made of $10,000. At the end of the year, $500 in nonqualifying dividends has been received and the value of the investment is $10,500. If the investor is in the 30% tax bracket, the after-tax yield is A) 3.5% B) 6.5% C) 8.5% D) 5.0%

A *The only return (as far as yield is concerned) is the $500 of dividends. Remember, nonqualifying dividends do not "qualify" for the 15% rate. Subtracting 30% for taxes leaves $350 which, when divided by the $10,000 initial cost, is an after-tax yield of 3.5%. If the question had asked about total return, then the $500 unrealized profit would have been included, although there would have been no tax on it.

An investor purchases a 5% callable convertible subordinated debenture at par. Exactly one year later, the bond is called at $104. The investor's total return is A) 9%. B) 5%. C) 4%. D) 7.5%.

A *Total return consists of income plus gain. Buying a bond at par and having it called at $104 results in a $40 gain. With a 5% coupon, there will be two semiannual interest payments of $25 in a one-year holding period. Adding the $40 + $50 = $90 total return on an investment of $1,000 which = 9%.

During your annual review with a client, you go over all the year's transactions. The beginning of the year balance in the account was $3,000. The client purchased 100 shares of ABC on February 1 at $30 per share and sold it on June 1 at $33 per share. During that period, ABC paid 1 quarterly dividend of $.30. The client used the proceeds of the ABC sale to purchase 66 shares of DEF on June 15 at $50 per share and sold it on December 15 at $60 per share. DEF pays quarterly dividends of $0.25 on the 1st of each month on a cycle beginning with February. Based on this information, you would inform the client that the account's total return is A) 34.10% B) 102.70% C) 46% D) 100%

A *Total return in an account is computed by taking all income plus capital gains and dividing that by the original investment. In this example, the client received a $0.30 dividend on 100 shares ($30) and two $0.25 dividends (August 1 and November 1) on 66 shares ($33). Add that $63 of income to the gain of $300 on the first transaction, and $660 on the second, to come up with a total of $1,023 divided by $3,000, which equals a total return of 34.1%.

One of the important roles of an investment adviser representative is assisting clients in analyzing the performance of securities held in their portfolios. Which of the following is the best measurement of a security's performance? A) Total return B) Standard deviation C) Beta D) Yield

A *Total return reflects the entirety of a security's performance because it includes both income and capital appreciation. Beta and standard deviation are risk measurements, and while they may be used to evaluate a security's performance when compared to the risk taken, they don't truly provide a measurement as does total return.

An investor is of the opinion that the recent bull market has run its course, and she wants to protect her portfolio consisting largely of equities with a market cap of less than $1 billion. Her best choice would be to A) buy puts on the Russell 2000. B) sell futures on the Russell 2000. C) sell puts on the S&P 500. D) buy puts on the S&P 500.

A *When a bull market runs out of steam, a decline usually follows. The best way to protect her positions is purchasing a put option on a benchmark that represents her holdings. Because this investor's portfolio is so heavily invested in small-cap stocks, the appropriate benchmark for hedging would be the Russell 2000.

If an agent recommends that a client invest a portion of his portfolio in an international stock fund and is asked whether she should compare the performance of the fund against the S&P 500 Index, how should the agent respond? A) There is no appropriate benchmark against which an investor can compare a portfolio of foreign securities. B) No, it is preferable to compare the fund against the Morgan Stanley Capital International Europe, Australasia, Far East (EAFE) Index because it covers international securities. C) No, it is preferable to compare the fund against the Russell 2,000 Index because it covers smaller corporation stocks. D) Yes, the S&P 500 is an appropriate benchmark against which to compare the performance of all equity funds.

B *It is important that a particular mutual fund be compared against the appropriate benchmark. An international fund's performance should be compared against an index of foreign stocks such as the Morgan Stanley Capital International Europe, Australasia, Far East (EAFE) Index.

One measure of an investor's total return is called holding period return. The computation includes both income and appreciation and is used for both debt and equity securities. An investor's holding period return would exceed the bond's yield to maturity if A) the bond was redeemed at a discount B) the coupons were reinvested at a rate exceeding the yield to maturity C) the bond was called at a premium D) the investor purchased a put option on the bond

B *The calculation of yield to maturity assumes reinvestment of the bond's interest at the coupon rate. Therefore, if the investor were able to do better than that, the holding period return would be increased. This is part of the concept of internal rate of return (IRR) which takes into consideration the time value of money (compounding). It is tempting to answer a call at a premium and that might, in fact, increase the total return, but we have no idea when the call takes place, at what price and the original purchase price of the bond. Just keep it simple - if the question says you can earn more than the YTM, your return will be higher than the quoted YTM.

When a bond is selling at a premium, a bond callable at par will A) have a YTM that is more than the coupon B) have a YTC that is more than the coupon C) have a YTC that is less than the YTM D) have a current yield that is less than the YTM

C *A bond selling at a premium will always have a yield that is lower than the coupon. Highest of the computed yields will be the current yield because, unlike the YTM or the YTC, the loss at payoff of the principal is not included. Comparing YTM and YTC, because in both cases the investor is getting back the same par value, the YTC is lower because the loss is occurring sooner (bonds are always called prior to maturity).

Bill will put money into stocks only if he expects that stock returns, over time, will outpace bond returns by some amount that compensates him for the added volatility of owning stocks. This reflects A) premium priced bonds B) option premium C) risk premium D) time premium

C *Investors will put money into stocks only if they expect that stock returns, over time, will outpace bond returns by some amount that compensates them for the added risk of owning stocks. This extra return from stocks is known as risk premium-literally, the premium an investor receives in exchange for owning a riskier, more volatile instrument.

During the past year, the market price of Kapco common stock has increased from $47 to $50 per share. Over that period, Kapco's earnings per share (EPS) have increased from $2.00 to $2.50 per share, and their dividend payout ratio has decreased from 50% to 40%. Based on this information, the current yield on Kapco common stock is A) 4.26% B) 2.13% C) 2% D) 6.34%

C *The current yield on a stock is computed by dividing the annual dividend rate by the current market price. With EPS of $2.50 and a 40% payout ratio, the annual dividend is $1.00. This dollar divided by the current market price of $50.00 results in a current return of 2%.

Which of the following indices or averages is based on the prices of only 65 stocks (30 industrial, 20 transportation, and 15 utility)? A) Value Line B) S&P Composite C) Dow Jones Composite Average D) Wilshire 5,000

C *The most widely quoted and oldest measures of changes in stock prices are the Dow Jones averages. They are also the smallest in terms of the number of stocks included in the averages with only 65 stocks. It is the only price-weighted index on the exam; all of the others are cap-weighted.

A client purchased a security for $60 and sold it 1 year later for $59. If he received 4 quarterly dividends of $0.50 each during the period, his total percentage return would be A) 3.30% B) 0% C) 1.67% D) 2%

C *The total return on an investment is the sum of the capital gains/losses plus any income distribution such as dividends or interest. In this case, the client had a capital loss of $1 ($60 − $59 = $1), which was offset by $2 (4 × $0.50 = $2) in dividend distributions for a total dollar return of $1. In percentage terms, the return is calculated by dividing the dollar return amount by the total invested or $1 divided by $60 = 1.67%.

On June 20, 2016, an investor in the 30% marginal federal tax bracket acquired a growth stock paying no dividend for $10 per share. On June 22, 2017, the investor sold the stock for $20 per share. Presuming capital gains rates are 15%, the investor's after-tax rate of return is closest to A) 70% B) 100% C) 200% D) 85%

D *Although the stock grew at a 100% rate of return (by doubling), the investor must pay capital gains tax on the investment at 15%, and the investor realizes an after-tax rate of return of approximately 85%. Because the investor held the stock for more than 1 year, the sale is taxed at a favorable capital gains rate rather than at the investor's ordinary income tax rate.

An investor owns a common stock that has been paying a dividend at an annual rate of $2.00. If the investor buys 100 shares of the stock at $50 and sells it 3 months later for $52, the approximate annualized rate of return is A) 4% B) 12% C) 5% D) 20%

D *Annualized rate of return is computed by taking the investor's total return and annualizing it. In this case, the investor had $2 of appreciation and $0.50 (1 quarter) in dividends. Total return of $2.50 divided by the $50 cost is 5%. But, that is for 3 months − 1 quarter. Multiply that by 4 to get the annual rate.

In order to compute a client's realized holding period return, it is not necessary to know A) the original investment B) value at the end of the holding period C) income received during the holding period D) paper losses

D *The question is asking for realized return. That means that we ignore paper losses, (just another term for unrealized loss).

When an investor's original value is subtracted from the ending value, and then has the income received over that time period added to it, which is then divided by the original cost, the result is A) internal rate of return B) annualized return C) expected return D) holding period return

D *This is the method of computing holding period return.

Expressed as a percentage, what is the total return on a 1-year, newly issued (365 days to maturity) zero coupon debt obligation priced at 95? A) 5% B) The return cannot be determined without knowing current interest rates. C) 5.26% plus the implied coupon rate D) 5.26%

D *Zero coupon bonds get their name from the fact that there is no coupon interest paid. The investor's return is the difference between the discounted price paid and the $1,000 maturity value. In this question, the price paid was 95 ($950) and the maturity value is $1,000. That $50 difference is the investor's return. To determine the total return percentage on this zero coupon debt obligation, the $50 capital appreciation is divided by the cost of the bond, in this case $950, for a total return of 5.26%. Total return of a zero coupon security is made up entirely of the difference between the cost of the security and its sale or maturity price. The market price of the security, not current interest rates, is used in the calculation of total return.