Measures of Investment Returns

Question 1

simple vs compound return

Answer 1

simple return: arithmetic mean (may not reflect actual return outcome for investors)

compounding return: involves adding interest to principal in order to calculate interest in their next period

Question 2

Geometric mean

Answer 2

Geometric mean: (time weighted return) reflects compound returns over more than one time period
- used to find average of numbers as percentages
- used to measure change of wealth over multiple periods
- used to evaluate performance of investment manager

Question 3

Geometric mean calculation

Answer 3

1. Add 1 to the returns expressed as a decimal ( 25%, 1.25: 15%, 1.15: -12%, .88
2. Multiply the returns results of step 1
3. The result of step 2 becomes the FV
4. -1 is always PV
5. N is the number of years of the investment
6. solve for i

Question 4

Time weighted return

Answer 4

measures investment performance (income and price changes) as a percentage of capital at work
- eliminates effects of additions and withdrawals and their timing that distort dollar weighted return

Question 5

Dollar weighted return

Answer 5

measures change in total dollar value, treating additions and withdrawals of capital as part of the return along with income and capital gains and losses
- IRR/NPV
- enables investors to compare absolute dollar amounts with financial goals
- manager to manager comparison not possible

Question 6

Real rate of return

Answer 6

(inflation adj. interest rate)
- nominal rate of return adjusted for inflation
IRR = [(1+after tax return / 1+inflation rate) -1] * 100

Question 7

Nominal return

Answer 7

actual returns produced over a given time period without accounting for the purchasing power of the dollar inflation

Question 8

Total return

Answer 8

annual return on an investment including appreciation or loss and dividends or interest

Question 9

Risk adjusted return

Answer 9

return has been altered to account for the difference in risk among variables of the same type

Question 10

Holding period return (HPR)

Answer 10

• total return over period from purchase to end of period or sale dividend (end of period) by the price of the investment
• weakness: fails to consider the timing of when the cash flow occurred. if the time period is over 1 year, the HPR overstates the true annualized return. less than one year then understates
• calculate: income + price appreciation + dividends ( margin interest + -purchase price) / purchase price
  Return / Basis = HPR

Question 11

Internal Rate of Return (IRR)

Answer 11

• discount rate at which the present value of future cash flows equals the cost of the investment
• when the NPV of cash flow is zero, the discount rate being used is the IRR
• when IRR > required return its a good investment

Question 12

Yield to maturity

Answer 12

• effective yield of a bond
• compounded rate of return an investor will receive from a bond at the current market price if held to maturity
• accounts for market price and capital gains or losses on bond if held to maturity
• always use semiannual compounding, even with 0 coupon bonds

Question 13

YTM and reinvestment rate risk

Answer 13

• YTM assumes bond holder reinvests all coupons received from a bond at a rate equal to its computed YTM
• if investor spends coupon or reinvests them at a rate different than YTM then realized yield will be different from YTM
• zero coupons eliminate reinvestment rate risk

Question 14

Yield to call

Answer 14

presumes that the bond will be redeemed by the issuer at the first call date specified in the indenture agreement
- most corporate and some government bonds are callable
- essentially same as YTM except the principal value at maturity is replaced by the call price and maturity date (years) is replaced by the first call date

Question 15

Current yield

Answer 15

• takes into account the interest in dollars and current market price of the bond
• does not factor any discount or premium
  CY = annual interest in dollars / bonds current price

Question 16

Taxable equivalent yield (TEY)

Answer 16

• interest rate on taxable bonds necessary to provide same after-tax return as a muni

TEY = ( tax exempt yield) / (1 - tax rate)
or
tax exempt yield = TEY * (1 - tax rate)