Section 103 Unit 6

Question 1

Simple Rate of Return

Answer 1

A simple rate of return for an investment is computed by dividing its total return (income earned plus capital appreciation divided by the original investment) by the number of years that the investor has held the asset.

E X A M P L E Jacob owned an investment that generated a total return of 60% over the past five years. Jacob’s simple rate of return is 12% (60% ÷ 5).

Question 2

Compound Rate of Return

Answer 2

The compound rate of return computation for an investment assumes that all interim proceeds, such as interest and repayment of principal, are reinvested (thereby generating additional return) over the holding period.

E X A M P L E Melissa deposits $1,000 in a one-year CD that pays an annual interest rate of 4% compounded quarterly. You have determined that, at the end of one year, Melissa will have a total of $1,040.60 ($1,000 +/−PV; 1 × 4 N; 4 ÷ 4 I/YR; solve for FV). Therefore, Melissa’s compound rate of return is 4.06% ($1,000 +/−PV; $1,040.60 FV; 1 N; solve for I/YR).

Question 3

Arithmetic Mean

Answer 3

The arithmetic mean is calculated by dividing the sum of the periodic returns by the total number of periods being evaluated.

Year 1:	15.20%
Year 2:	9.10%
Year 3:	6.50%
Year 4:	18.30%
Year 5:	16.80%
 	       65.90%
 65.90%/5=13.18
Arithmetic mean is the same as the average, or mean, return we used in the last unit when we computed various measures of investment risk. The arithmetic mean is a noncompounded return; it does not assume reinvestment of returns.

Question 4

Geometric Mean

Answer 4

The geometric mean, unlike the arithmetic mean, assumes compounding of returns.
E X A M P L E Continuing with the returns in the previous example, the geometric mean of 13.09% may be computed as follows:
PV = –$1 (just part of the equation)
FV = $1 (1 + 0.152)(1 + 0.091)(1 + 0.065)(1 + 0.183)(1 + 0.168) = $1.8495
n = 5
Solve for i = 13.0865 = 13.09%

geometric mean will always be lower than the arithmetic mean, except when the returns for all periods are equal, in which case the geometric and arithmetic means will be equal.

Question 5

Time-Weighted

Answer 5

A time-weighted return is determined without regard to any subsequent cash flows of the investor. As such, it is a measure of the performance of the investment over a period of time (and not of the investor as in a dollar-weighted approach). Most returns reported on mutual funds are time-weighted because the portfolio manager does not have any control over the future cash flows to the fund with respect to investor dollars.

CF0 = –$50 (value of the stock at the beginning of the investment period)
CF1 = $4 (dividend paid on stock at end of year 1)
CF2 = $75 (value of stock at the end of year 2)
Solve for IRR = 26.54%

Question 6

Dollar-Weighted Return

Answer 6

A dollar-weighted return considers subsequent contributions to and withdrawals from an investment, including sales of, for example, stock. As a result, the dollar-weighted approach focuses on the return of the investor (not the investment, as in the time-weighted approach) over a period of time, and usually results in a different rate of return than does the time-weighted method.

CF0 = –$50 (value of the stock at the beginning of the investment period)
CF1 = $4 – $65 = –$61 (dividend less purchase of additional stock)
CF2 = $75 × 2 = $150 (value of stock holdings at the end of year 2)
Solve for IRR = 22.63%

Question 7

Nominal Rate of Return

Answer 7

Is simply its stated rate of return for a given period without accounting for inflation. Also reflects the before-tax rate of return. NO FORMULA NECCESSARY IT IS THE EXPTECTED RATE OF RETURN

Question 8

Real Rate of Return

Answer 8

The real rate of return takes inflation into account; that is why the real rate of return is sometimes called the inflation-adjusted rate of return.

E X A M P L E Renee owns a corporate bond with a coupon rate of 6.00%. If the annual inflation rate is 3.5%, her real rate of return on the bond is 2.42%, calculated as follows:

(((1+0.06)/(1+0.035))-1)x 100 = 2.42 (rounded)

Question 9

After-Tax Inflation-Adjusted Rate of Return

Answer 9

A two-step process may be used to integrate the effect of taxes and inflation on an investment’s rate of return.
1.
Compute the after-tax rate of return by using the formula: r after-tax = r nominal × (1 – investor’s marginal tax rate)

If the investor resides in a state that imposes state income taxes, the marginal tax rate should also reflect state taxes (in addition to federal taxes).
2.
Multiply the nominal rate by (1– investor’s marginal tax rate) and use this product as the numerator in the inflation-adjusted rate of return formula and derive the after-tax, inflation-adjusted amount.

Question 10

Annual Percentage Rate (APR)

Answer 10

The nominal annual percentage rate (APR) is the yearly cost of funds expressed as a percentage. However, the nominal APR does not take compounding into consideration. If a lender advertises a 1.25% monthly rate, the APR is 15% (1.25% × 12).

Question 11

Effective Annual Rate (EAR)

Answer 11

The effective annual rate (EAR) is the annual percentage rate taking into consideration the impact of compounding. This calculation provides the annual rate of interest of an investment or debt when compounding occurs more than once per year.
effective annual rate = [1 + (i ÷ n)]/\n – 1

Question 12

Total Return

Answer 12

Total return may be thought of as the sum of:
The capital appreciation/depreciation on the underlying principal of the investment; and
Any income or earnings generated from that investment.

Question 13

SEC Yield

Answer 13

The SEC yield is a standardized calculation that the SEC requires mutual funds to report and allows investors to compare yields among various investments. This yield is based on the most recent 30-day period covered by the fund’s SEC filings and represents the interest and dividends earned during that particular period, after expenses have been deducted. Mutual funds are required to disclose this rate in their prospectuses.

Question 14

Holding Period Rate of Return (HPR)

Answer 14

The holding period rate of return (HPR) (sometimes referred to as the single period return) is simply the total return of an investment for the given period over which the investment is owned. However, the measurement has a major weakness because it fails to consider the timing of when the cash flows actually occurred. As a result, if the holding period of the investment is more than one year, the HPR overstates the true return of the investment on an annual basis. Conversely, if the investment’s holding period is less than one year, the HPR understates the true return.

Question 15

The Formula for the Holding Period Return (Single Period Return)

Answer 15

HPR = (ending value (EV) – beginning value (BV) ± cash flows (CF)) / beginning value (BV)

Question 16

Current Yield (CY)

Answer 16

The current yield (CY) of a bond is the return represented by the amount of interest income paid in relation to the current market value of the bond. Current yield is calculated by dividing the annual interest payment on the bond (as reflected by its coupon rate multiplied by the par value of the bond) by the bond’s current market price.

Question 17

Yield to Maturity (YTM)

Answer 17

The yield to maturity (YTM) of a bond takes into account both the market price of the bond and any capital gains or losses on the bond if it is held to maturity. A major assumption when calculating YTM is that all interest payments on the bond are reinvested at the calculated YTM. For example, if the calculated YTM is 7%, any interest payments generated from the bond are also assumed to be reinvested at 7%.

Question 18

YTM Formula

Answer 18

PV = CMV
FV = Par Value
PMT = Annual Coupon Payment (Unless semiannual or Quarterly)
N = Number of Periods

Question 19

Yield to Call (YTC)

Answer 19

The yield to call (YTC) on a bond takes into account the possibility that the bond may be called by the issuer before its maturity date. The actual formula for YTC is the same as that for YTM except that the par value of the bond is replaced by the call price and the maturity date is replaced by the first potential call date.

Question 20

YTC Formula

Answer 20

PV = CMV
FV = Call Price
PMT = Annual Coupon Payment (Unless semiannual or Quarterly)
N = Periods until called

Question 21

Taxable Equivalent Yield (TEY)

Answer 21

TEY = Tax exempt yield / 1 - marginal tax rate