Investment Planning: Measures of Investment Returns (Module 6)
Time-weighted Return
is a return based on portfolio growth from one period to the next.
Dollar-weighted Return
is a return based on the initial value plus investments versus ending value.
An investor pays $875 for a bond with an annual coupon of 6%. There is exactly 7 years to go before the bond matures. Assuming that the investor does hold the bond until maturity, what is the HPR of the bond?
$1,000 - $875 + 420 / 875 = 62.3% In reference to point (1), this could have been asked as a capital appreciation and income yield component: $1,000 - $875 / $875 = 14.3% (Capital gain component) and $420 (7 coupon payments x $60) divided by $875 = 48%. The two together would sum to the total of 62.3%.
If an investor bought a call option for $400 two weeks ago, and sold the option today for $540, what would the HPR be?
$540 - $400 / $400 = .35 = 35%
Kerry held an S&P Index Fund for three years. Her returns during that time were 20%, -10%, and 5% respectively. What was her arithmetic mean return?
(1/3)(.20 -.10+ .05) = .05 or 5%
Real Rate of Return: Formula (Quick)
(NR - CCL) is approximately equal to RR NR = nominal rate of return CCL = change in cost of living
What are the three conditions must be met in order for the bondholder to earn the bond's YTM?
- Bond must be held to maturity. - Issuer does not default in timing of payments. - Payments are immediately reinvested at YTM.
Total return represents the growth or depreciation of an investment. What are the two key components?
- Capital appreciation or depreciation - Dividends or interest
Which of the following is true about YTM & YTC? 1. YTM is based on maturity date of the bond 2. YTM is appropriate for callable bonds 3. YTC is appropriate for non-callable bonds 4. YTC is based on first callable date
1 & 4
Jed was in the 31% tax bracket and his taxable investments had a total return of 45%. What was his after tax return?
45%(1-.31) = 31.05%
Todd buys $20,000 of stock on margin. He deposits $10,000 with the brokerage firm. The interest on the margin account is 12% compounded quarterly. If he sells the stock exactly one year later for $25,000, how much does he make? a. $3,745 b. 38% c. $3,900 d. 24.9%
A 12% annually or $1,200. $25,000 - ($10,000 + $1,255) - $10,000 = $3,745
Jim has asked you to evaluate the following bonds. He is in a 31% marginal tax bracket. On a tax equivalent basis, which of the bonds provides the best return? a. Municipal bond paying 5.5% b. Treasury zero bond paying 6.5% c. Corporate zero bond paying 7.5% d. Corporate bond paying 7.8%
A The zero's interest is taxable each year. It is not deferred. The tax equivalent yield of the municipal bond is 5.5% / 69% = 7.97%.
Don Watson recently purchased a bond for $1,135 with a 10% coupon. It will mature in 10 years but can be called in 5 years at $1,100. What is its YTM / YTC? a. 8.01% / 8.30% b. 8.40% / 8.28% c. 7.72% / 8.01% d. 9.44% / 9.09%
A YTM: 1135 CHS PV 1000 FV 100 ENTER 2 + PMT 10 ENTER 2 x N i 2 x YTC: 1135 CHS PV 1100 FV 100 ENTER 2 + PMT 5 ENTER 2 x N i 2 x
Mrs. Turner lives in a state imposing a state income tax of 6%. Her federal income tax rate is 28%. Which of the following bonds gives her the best return? a. A municipal bond (issued in her state) paying 5.2% b. A municipal bond (issued in another state) paying 6.4% c. A corporate bond paying 7.8% d. A treasury bond paying 7%
B Compare the other options to the muni at 5.2%: Treasury = 7% x (1 - 0.28) = 5.04% Corporate = 7.8% x [1 - (0.28 + 0.06)] = 5.148% Out-of-State muni* = 6.4% x (1 - 0.06) = 6.016% *This bond is still subject to state income taxes. The 5.2% is tax-exempt yield. All the other answers must be converted to tax-exempt yield.
Tom Baker invests $25,000 in a stock. Five years later he sells the stock for $40,000. He is in a 15% tax bracket when he sells the stock. Over the five year period, inflation increased by 3.5%. He wanted to achieve a "real rate of return" of 5% over the five year period. Did he? a. No b. Yes
B Using TVM calculation: $25,000 ± PV, $40,000 FV, 5N I = 9.856% Real rate of return is the inflation-adjusted interest rate. HP 10B Calculator Keystrokes: 1.09856 ÷ 1.035 -1 x 100 = 6.14 HP 12C Calculator Keystrokes: 1.09856 enter, 1.035, ÷, 1, -100, x, i = 6.14
Steven recently purchased a zero-coupon bond for $375. It will mature in 14 years, at which time it will be worth $1,000. What is the yield to maturity? a. 7.42% b. 7.26% c. 7.13% d. 7.01%
C 375 CHS PV 1000 FV 14 ENTER 2 x n i 2 x
Sherry recently purchased a bond for $950 with a 6% coupon. It will mature in 20 years, but it can be called in 10 years at $1,050. What is the yield-to-call? a. 6.87% b. 7.28% c. 7.06% d. 6.69%
C 950 CHS PV 1050 FV 10 ENTER 2 x n 60 ENTER 2 / PMT i 2 x
What is the biggest weakness of the dollar-weighted return (assuming constant)? a. Inflation rates b. Purchasing power rates c. Reinvestment rates d. Interest rate
C Dollar-weighted return is an IRR calculation. The calculation assumes that the reinvestment rate is yield to maturity. If the interest is spent or reinvested at a lower/higher rate, the yield will be different than the IRR calculated.
A client purchased Steel, Inc., for $20,000. The stock paid a $1,000 dividend per year. The client sold the stock for $25,000 after two years. What is the holding period return? a. 25% b. 20% c. 35% d. 30%
C HPR = ($25,000 + $2,000 - $20,000) / $20,000 = 35%
Helen is in a 15% federal marginal tax bracket and pays 6% state income tax. She has $20,000 to invest. Her bond choices are the following. What is her best choice? a. Her state's municipal paying 6.5% b. Corporate bond paying 8% c. Another state's municipal paying 7%
C Tax-exempt yield (I) = 8% x (1 - 0.21) = 6.32% Tax-exempt yield (II) = 7% x (1 - 0.06) = 6.58%
What is the current yield if a $1,000 bond with a 7% coupon is now selling for $1,050? a. 7.33% b. 7% c. 6.67% d. 6.23%
C This is a premium bond. Current yield will be less than coupon rate. Current Yield = $70 / $1,050 = 6.67%
Mrs. Bean lives in Manhattan. She is in a 28% federal tax bracket and pays 10% NY state tax and 5% NY city tax. If she purchases Treasury bonds that pay 10%, what is her after-tax rate of return? a. 10% b. 8.5% c. 7.2% d. 5.7% e. 6.2%
C Treasuries are not subject to state or city taxes but are subject to federal tax. 10% (1 - 0.28) = 7.2%
Don Watson recently purchased a bond for $1,135 with a 10% coupon. It will mature in 10 years, but can be called in 5 years at $1,100. He sells the bond in two years for $1,200. What is the holding period return? a. 14.53% b. 5.70% c. 23.35% d. 26.50%
C [($1,200 + $200) - $1,135] / $1,135 = 23.35%
Which of the following scenarios would lead to realization of YTM for a bond? 1. The bond is held to maturity; coupons are reinvested immediately at YTM; all payments are received on time. 2. The bond is called by the issuer due to a low interest rate environment. 3. The bond is held to maturity; coupons are reinvested immediately realized at a compound yield different than YTM; all payments are received on time. 4. The bond is a zero coupon bond and is held to maturity; par payment is received on time.
Correct Answer: 1 & 4 Explanation: For YTM to be realized, the bond must be held to maturity, the issuer must make full payments of coupon and par on time, and the cash flows must be reinvested immediately at YTM. Pure-discount (zero coupon) bonds do not have cash flows to reinvest, so if held to maturity, the holder earns YTM.
The total return for XYZ fund for one year is 2%. For the year, interest income was 6%, and there was a 4% loss in principal. Which of the following statements are true? 1. Assuming that the fund's interest is not reinvested, the price at the end of the year was lower than the beginning 2. The fund did not pay any interest because it had a negative return 3. The fund paid 2% interest 4. The interest was assumed to have been reinvested
Correct Answer: 1 & 4 Explanation: The total return for the fund was 2%, which was comprised of a 4% loss of principal, and a 6% interest payment. Using the HPR formula, and assuming a starting value of $1,000, we would calculate the total return as ($960 + $60 - $1,000) / $1,000 = 2%.
The quarterly returns for Fred's portfolio are 2.5%, 1.7%, -3.6% and 2%. What was the annualized return of his portfolio using the compounding method? A. 2.5% B. 4.026% C. .10% D. -3.2%
Correct Answer: A. 2.5% Explanation: Return = [(1+.025)(1+.017)(1-.036)(1+.02)]-1 = 2.5%.
Jill Edwards purchased 1,000 shares of ABC mutual fund for $10.00 per share, for a total investment of $10,000. A short time later the fund paid a $550 dividend, which Jill decided to have reinvested back into the fund. At the time of the reinvestment, ABC fund was selling for $11.00 per share. At the present time, ABC fund is worth $13.70 per share. What is the holding period return (HPR)? A. 43.85% B. 36.35% C. 24.54% D. 15.5%
Correct Answer: A. 43.85% Explanation: The $550 dividend was reinvested at a price of $11.00, increasing the number shares owned to 1,050. ($550 / $11.00 = 50 shares). Therefore, the value of the dividend is imbedded in the ending account value of $14,385 ($13.70 x 1,050 shares). In this case, the HPR would simply be the price at the end, minus the price at the beginning, divided by the price at the beginning. Plugging in the numbers, the calculation yields: {($14,385 - $10,000) / $10,000} = .4385 = 43.85%
The following data are available on the returns of the Smith Tinker Corporation (STC) for the past 4 years: Y1 = 10%, Y2= -1%, Y3= 15%, Y4= 12%. The arithmetic return on the STC stock is 9%. Calculate the GMR on the stock. A. 4.4% B. 8.8% C. 9.4% D. 8.2%
Correct Answer: B. 8.8% Explanation: The geometric mean return from this 4-year investment is calculated as follows: GMR = [(1.10)(.99)(1.15) (1.12)]^.25 = 8.8%
Molly is trying to decide between purchasing a corporate bond paying 8%, a bond fund paying 30-day net annualized yield of 7.2%, and a municipal bond fund paying 5.5%. If Molly is in the 28% tax bracket, which option would translate into the biggest after-tax yield for her? A. Bond Fund B. Corporate Bond C. Municipal Bond Fund
Correct Answer: B. Corporate Bond Explanation: The tax equivalent yield for the municipal bond at Molly's tax bracket is 7.638%. Although it is higher than the bond fund, it is not as high as the corporate bond. If Molly was basing her decision purely on how much yield she would receive, the corporate bond would be the best investment choice.
Consider a $10,000 bond paying a 3.5% annual coupon rate for 10 years. The bond's present value is $8,140.32, if its cash flows are discounted at the YTM of 6% per year (or 3.0% per 6-month period). The bond's yield-to-call is 9.373% at an annual rate. What will you consider to make the buy/sell decision for the bond? A. Present value = $8,140.32 B. Yield to maturity = 6% C. T = 10 years D. Yield to call = 9.373%
Correct Answer: B. Yield to maturity = 6% Explanation: After computing the two different yields, you must select the lower yield for investment decision-making purposes, because that return represents the minimum yield that the investor can expect to earn.
Which of the following statements concerning bond yields is incorrect? A. Nominal yield is higher than current yield for a premium bond. B. Yield to maturity is higher for a premium bond than for a discount bond. C. If the realized compound yield is less than YTM, then the bondholder will earn less than the YTM. D. Bond Equivalent Yield converts discount debt instrument yields to a yield similar to a semi-annual coupon paying bond.
Correct Answer: B. Yield to maturity is higher for a premium bond than for a discount bond. Explanation: YTM does depend on whether the bond is selling at a premium or a discount. YTM is less for a premium bond because the premium is amortized over the remaining years to maturity, so less money is available for compounding. If a bond is selling at a premium, then the nominal yield is divided by a larger price to obtain the current yield, therefore the current yield would be lower. If the bondholder reinvests cash flows at a rate below YTM, there will be less interest to compound. Bond equivalent yield makes a pure discount bond's yield equivalent to a coupon paying bond.
Fred had $20,000 in his portfolio at the beginning of the year. He added $5,000 to the portfolio in the middle of the year. The account value before he added the $5,000 was $19,178 and at the year-end, it was $25,998. What was the annual time-weighted return for Fred's portfolio? A. 20.89% B. 3.992% C. 3.108% D. 20%
Correct Answer: C. 3.108% Explanation: The return for first half year = ($19,178 - $20,000)/$20,000 = -.0411. The return for second half year = ($25,998 - $19,178 - $5,000) /($19,178 + $5,000) = .075275. The time-weighted return = [(1-.0411)(1+.075275)-1] = .03108 or 3.108%.
The following data are available on the returns of the Smith Tinker Corporation (STC) for the past 4 years: Y1 = 10%, Y2= -1%, Y3= 15%, Y4= 12%. What is the arithmetic return on the STC stock? A. 4% B. 15% C. 12% D. 9%
Correct Answer: D. 9% Explanation: The arithmetic mean return (AMR), an average of historical one-period rates of return, is computed as follows: AMR = [10+(-1)+15 +12]/4 = 9%
Which of the following reasons make the dollar-weighted return inappropriate for evaluating a portfolio? 1. The return is strongly influenced by the size and timing of the cash flows. 2. The investment manager typically has no control over the deposits and withdrawals. 3. The market value of the portfolio is used just before each cash flow occurs. 4. Return reflects growth of the dollar from the beginning.
Correct Answers: 1, 2 Explanation: In general, the dollar-weighted return method of measuring a portfolio's return for purposes of evaluation is regarded as inappropriate. The reason behind this view is that the return is strongly influenced by the size and timing of the cash flows (namely, deposits and withdrawals), over which the investment manager typically has no control.
Current Yield: Formula
Current Yield = Dollars of coupon interest per year/Bond's current market price
The annual returns for XYZ common stock have been +18%, +10% and -30%. What was the geometric mean over the three years? a. -5.03% b. 0.67% c. 1.23% d. -3.14%
D 1.18 x 1.10 x 0.7 = 0.9086 FV 0.9086 FV, 1 ± (CHS) PV, 3N = -3.14%
Beth (35% marginal tax bracket) bought 1,000 shares of Tech Inc. over a year ago for $40,000. It paid $1,000 of qualified dividends over the time she owned it. She just sold it for $60,000. What was her after-tax holding period return? a. 52.5% b. 45% c. 34.13% d. 44.63%
D 60000 + 1000 - 40000 = 21000 gain 21000 x 0.85 = 17850 17850/40000 = 44.63%
Holding Period Return (HPR): Formula
HPR = (P1 + D - P0) / P0 This does not assume reinvestment of dividends
What would Kerry's geometric return be if her portfolio yielded -20% return in year one, 40% in year two and 20% in year three?
Keystrokes .80 ENTER 1.40 x 1.20 x 3 1/x yx 1 - The calculator returns: .10357 (which is also expressed as 10.357%)
Kerry held an S&P Index Fund for three years. Her returns during that time were 20%, -10%, and 5% respectively. What was her geometric mean return?
Keystrokes 1.20 ENTER .90 x 1.05 x 3 1/x yx 1 - The calculator returns: .0428 (which is also expressed as 4.28%)
Consider a bond that has $1,000 par and is selling currently for $1,065.90, pays semi-annual coupons of $50 (10% coupon), and matures in 1 and ½ years. What is its YTM?
Keystrokes 1000 FV 3 n 50 PMT 1065.90 CHS PV i The calculator returns: 2.68 2.68 x 2 = 5.37
Consider a $10,000 bond paying a 3.5% annual coupon rate for 10 years. The bond's present value is $8,140.32, if its cash flows are discounted at the YTM of 6% per year (or 3.0% per 6-month period). Whats the YTM?
Keystrokes 10000 FV 20 n 175 PMT 8140.32 CHS PV i The calculator returns: 3.00 3 x 2 = 6
Consider a $10,000 bond paying a 3.5% annual coupon rate for 10 years. The bond's present value is $8,140.32, if its cash flows are discounted at the YTM of 6% per year (or 3.0% per 6-month period). Assume the bond has a 7% call premium, which means it is callable at 107% of its par in 5 years (10 semi-annual periods). Whats the YTC?
Keystrokes 10700 FV 10 n 175 PMT 8140.32 CHS PV i The calculator returns: 4.686 4.686 x 2 = 9.37
yield to call (YTC)
Most corporate bonds, as well as some government bonds, are callable by the issuers, typically after some deferred call period. If a bond is likely to be called, then the yield to maturity calculation is unrealistic. In the case of callable bonds, a calculation of the promised yield to call (YTC) should be used instead.
The Tax Equivalent Yield (TEY): Formula
TEY = Tax Free Yield/(1 - Tax Bracket)
What is the difference between geometric mean & arithmetic mean?
The compound average rate of return (geometric return) is similar to the arithmetic mean return, except the geometric return, because it does take compounding into account, will always be less than the arithmetic return. The compound average rate of return is also called the geometric mean return (GMR), where the GMR is computed over T successive time periods.
yield to maturity (YTM)
The rate of return on bonds most often quoted for investors is the yield to maturity (YTM), which is defined as the promised compounded rate of return an investor will receive from a bond purchased at the current market price and held to maturity. assumes that all interest income will be reinvested at the same YTM that existed on the day the bond was initially purchased
Your client is considering purchasing one of the following several bonds. All the bonds will mature in exactly 5 years at par. Coupon Price Bond #1 5.875 98.76 Bond #2 6.500 101.39 Bond #3 7.875 107.35 Bond #4 5.375 96.64 Based on yield to maturity, which bond would you recommend?
YTM for Bond #1 is 6.167; YTM for Bond #2 is 6.173; YTM for Bond #3 is 6.145; YTM for Bond #4 is 6.166. A 5.875% coupon is $58.75 per year or $29.375 semiannual.
Real Rate of Return: Formula (long)
[(1+ NR) / (1 + CCL)] - 1 = RR NR = nominal rate of return CCL = change in cost of living
