Measures of Investment Return Flashcards
Geometric Average Return
-the average compounded rate of return per year over a multiyear period. -the best measure of an investment over time -most commonly used when evaluating the performance of portfolio managers since it uses a base of constant dollars.
Geometric Average Return
= ((1 + 15%) × (1 + (− 5%)) × (1 + 10%))1/3 - 1
Arithmetic Average Return =(15% + (-5%) + 10%)/3= 10%
Time-Weighted Return
-determined without regard to any subsequent cash flows of the investor and uses the geometric mean in computing the overall return. -measure of the investment over time -sometimes referred to as the return on the investment,
The time-weighted rate of return differs from the money-weighted rate of return as it does not depend on the value of particular cash flows. The time-weighted rate of return is a geometric mean return over the whole investment period:
TWRR=[(1+HPR1)×(1+HPR2)×…×(1+HPRT)]^1/T
When calculating the time-weighted rate of return you don’t need to know the number of shares that were bought/sold (this data is redundant). You only need to know the prices of stock in different periods and the value of dividends.
In the previous paragraph we learnt that the money-weighted rate of return gives different weights to different periods, while the time-weighted rate of return gives the same weights to different periods. Therefore, we should conclude that if an investment manager has full control of the timing of cash inflows and outflows, we should use the money-weighted rate of return.
It would be appropriate in the case of our private investments when it is us who decides what amounts we invest in every period. When the portfolio manager has little influence on the invested amounts, we should apply the time-weighted rate of return. This is the case with a fund manager, who doesn’t have control over how much the clients add to or withdraw from the fund.
Dollar-weighted return
-determined using the subsequent contributions to and withdrawals from the investment by the particular investor and uses the arithmetic return in deriving the overall return. -measures the investors annual rate of return -
Dollar-weighted returns clearly state your actual returns but do not clearly describe the investment’s performance independent of your deposits and withdrawals
Essentially the IRR.
Arithmetic Average Return
-the return of an investment in an average year over a multiyear period. -best used as a measure of average performance over a single period.
Real Return
-the return of an investment after accounting for annual inflation
[(1+inflation rate)/(1+growth rate)] - 1
Assume an investor purchases a stock on Jan. 1 of a given year for $75,000. At the end of the year, on Dec. 31, the investor sells the stock for $90,000. During the course of the year, the investor received $2,500 in dividends. At the beginning of the year, the Consumer Price Index (CPI) was at 700. On Dec. 31, the CPI was at a level of 721.
Step 1 is to calculate the investment’s return using the following formula:
Return = (Ending price - Beginning price + Dividends) / (Beginning price) = ($90,000 - $75,000 + $2,500) / $75,000 = 23.3% percent.
Step 2 is to calculate the level of inflation over the period using the following formula:
Inflation = (Ending CPI level - Beginning CPI level) / Beginning CPI level = (721 - 700) / 700 = 3 percent
Step 3 is to geometrically back out the inflation amount using the following formula:
Inflation-adjusted return = (1 + Stock Return) / (1 + Inflation) - 1 = (1.233 / 1.03) - 1 = 19.7 percent
Since inflation and returns compound, it is necessary to use the formula in step three. If an investor simply takes a linear estimate by subtracting 3 percent from 23.3 percent, he arrives at an inflation-adjusted return of 20.3 percent, which in this example is 0.6 percent too high.
Nominal Return
-an investments states or before-tax and before-inflation rate of return for a given period.
Holding Period Return
-illustrates the total return of the investment for the given period over which the investment is owned. -it Fails to consider the timing of when the cash flows actually occurred and hence the time value of money. -if calculating for more than one year, it overstates its true return on an annual basis. If under a year it understates.
So, HPR is the total return earned by an investor over a single period and it includes all cash flows occurring at the end of the period.
HPR is a valuable tool when you want to calculate the rate of return on an investment over one period assuming that no additions or withdrawals of money occur meanwhile.
However, how should we compute the rate of return on the portfolio over many periods if there are cash inflows and outflows?
In such a case, we have two alternative measurement tools at our disposal, that is:
the money-weighted rate of return, and
the time-weighted rate of return.
Net Present Value (NPV)
-the difference between an investment’s market value and its cost.
Internal Rate of Return (IRR)
-the rate of return that equates the present value of all an investments cash inflows with the present value of its outflows, producing a new present value between the town of them of zero.
The money-weighted rate of return is simply an internal rate of return (IRR). However, we use the term internal rate of return in the context of capital budgeting. In portfolio management, this measure is called money-weighted rate of return. How was this term coined? Well, the money-weighted return accounts for the value of cash flows in given periods. So, logically the values of particular cash flows affect the value of the money-weighted rate of return.
The money-weighted rate of return is calculated through equating discounted cash inflows to discounted cash outflows, but in the exam we’ll use Cash Flow and IRR worksheets.
In the previous paragraph we learnt that the money-weighted rate of return gives different weights to different periods, while the time-weighted rate of return gives the same weights to different periods. Therefore, we should conclude that if an investment manager has full control of the timing of cash inflows and outflows, we should use the money-weighted rate of return.
It would be appropriate in the case of our private investments when it is us who decides what amounts we invest in every period. When the portfolio manager has little influence on the invested amounts, we should apply the time-weighted rate of return. This is the case with a fund manager, who doesn’t have control over how much the clients add to or withdraw from the fund.
Yield to Maturity
-considers the current income generated by the bond as well as the change of its value from its purchasing price to the price at maturity. -When the bond is selling at a premium the YTM will be less than the coupon rate. -When the bond is selling at a discount the YTM will be more than the coupon rate.
Yield to Call
-The return on a bond that is held until it is called or retired by the issuer. -When the bond is selling at a premium the YTC will be greater than the YTM. -When the bond is selling at a discount the YTC will be less than the YTM.
