Measurement of Investment Return Flashcards
Holding-Period Return or HPR
The price at the end (P1) less the price at the beginning (P0), divided by the price at the beginning (P0), represents a capital appreciation (depreciation) figure. While the dividend, interest paid, or any cash flow received (D), divided by the price at the beginning (P0), represents an income yield component.
HPR = (P1 + D - P0)/P0
Arithmetic Mean Return
The arithmetic mean is simply the sum of the all of the returns. divided by the number of periods over which the sum total is calculated. This is also called the average, or average return.
Geometric Mean Return
The geometric mean is the average growth of an investment computed by multiplying n variables and then taking the nth –root. In other words, it is the average return of an investment over time, a metric used to evaluate the performance of a single investment or an investment portfolio.
Real (Inflation Adjusted) Return
RR = ((1 + NR) / (1 + Ri))-1
NR = Nominal Return
Ri = Inflation Rate
RR = Real return
Real Return Quick Method
RR = NR - Ri
quick estimation
Yield to Maturity (YTM)
The rate of return on bonds that is most often quoted for investors is the yield to maturity (YTM), which is defined as the discount rate that equates the present value of all the bond’s future cash flows with its current market price (purchase price). The YTM is the compounded rate of return of a bond.
Yield to Call (YTC)
Bond prices are calculated on the basis of the lowest yield measure. Therefore, for premium bonds selling above a certain level, yield to call replaces yield to maturity, because it produces the lowest measure of yield.
Callable bonds have an embedded option that the bond issuer may or may not find profitable to exercise. The uncertainty about whether or not the bond will be called forces the investor to evaluate each of the possible future scenarios:
First scenario: If market interest rates rise, then it is safe to assume the bond issuer will not find it profitable to exercise the call option. When the bond is not called, it is customary to assume the bond remains outstanding until its maturity date. In the event of this first outcome, the traditional YTM is the appropriate yield measure.
Second scenario: If market interest rates decline, then it would be profitable for the bond’s issuer to call the bond before it matures. To evaluate this second scenario, the bond’s Yield to Call (YTC) must be calculated.
After-Tax Yield
After Tax Yield (TEY) = Tax Free Yield / (1 - Tax Bracket)
Current Yield
The current yield of a bond measures an annual cash flow relative to the bond’s current market price. Retirees who live on investment cash flows, for instance, are interested in a bond’s current yield. The current yield is an accurate representation of what income you are earning based on the price you paid. If the bond is selling at par, then the current yield is the same as the coupon rate.
However, if a bond is selling at a premium, the current yield will be lower than the yield. On the other hand, if the bond is selling at a discount, the current yield will be higher than the original yield.
Dollar-Weighted Return
Difficulties are encountered when deposits or withdrawals occur sometime between the beginning and end of the period. One method that has been used for calculating a portfolio’s return in this situation is the dollar-weighted return (or internal rate of return).
Consider a portfolio that at the beginning of the year has a market value of $100 million. In the middle of the year, the client deposits $5 million with the investment manager, and subsequently at the end of the year, the market value of the portfolio is $103 million.
$100million= $ -5million /
(1+r) + $103million/(1+r)2
r = -.98%
The dollar-weighted average (r) is a semi-annual rate of return. It can be converted into an annual rate of return by adding 1 to it, squaring this value, and then subtracting 1 from the square, resulting in an annual return of -1.95%.
[1+(-.0098)]2 − 1 = -1.95%
Time-Weighted Return
Alternative to Dollar Weighted Return is the time-weighted return on a portfolio. This mechanism only concerns itself with the portfolio appreciation or depreciation in value from one period to the next. That is, all cash flows into and out of the fund are totally disregarded from the return data. Time-weighted return is the only acceptable method to display the results of a portfolio manager’s performance.
Dollar vs. Time-Weighted Return
You need to know that the only appropriate method for measuring a portfolio manager, investment advisor, or mutual fund manager, is with a time-weighted return. The reason is that they are not responsible for when an investor decides to add or withdraw funds from an investment. It is in fact, only time-weighted returns that are published for the mutual fund industry.
Dollar-weighted returns are totally appropriate for an individual investor, to measure their particular return, based on their particular experience of adding (reducing) funds when they did.
Example of Time Weighted and Dollar Weighted return
An investor is trying to decide between investment advisor Jones and investment advisor Smith. The investor decides to place funds with each advisor and monitor results for a while before committing to a long-term relationship.
Jones initially receives $100,000 and Smith receives $900,000. For the next year, the stock market does very well, and each advisor’s fund does equally well - up 50%. At this point, with the Jones portfolio worth $150,000, and the Smith portfolio worth $1,350,000, the investor decides to give Jones an additional $900,000 and Smith an additional $100,000. As far as the investor is concerned, they have now given both Jones and Smith $1,000,000.
The second year the stock market crashes and each advisor’s portfolio declines 50%. The final value (after two years) of the Jones portfolio is $525,000, and the final value of the Smith portfolio is $725,000. At the end of the second year, the investor (not knowing about time-weighted versus dollar-weighted) keeps Smith and fires Jones. The investor stated: “All I know is that I gave them each a million bucks; at the end of two years Smith had $725K while Jones only had $525k. Therefore, Smith did a better job.”
1) Calculate the dollar-weighted return and time-weighted return for each advisor’s portfolio.
2) Comment on the validity of the investor’s comment.
Answers:
Dollar-weighted (Jones):
Keystrokes: 100 CHS g CF0 900 CHS g CFj 525 g CFj f IRR — (45.0%)
Dollar-weighted (Smith):
Keystrokes: 900 CHS g CF0 100 CHS g CFj 725 g CFj f IRR — (15.6%)
Time-weighted (Both):
(up 50% in year 1 and down 50% in year 2)
[(1+ -.50) x (1+.50)] ½ -1 = (13.4%)
The investor’s comment is not valid because on a time-weighted basis, both advisors had an equal return of (13.4%), which was solely based on a positive return of 50% in year one, and a 50% loss in year two.
While it is true that on a dollar-weighted basis Smith outperformed Jones, it was only true because Smith got the big chunk of the investment prior to the good year, and only a small portion prior to the bad year. The opposite was true for Jones. This demonstrates the point that investment advisors, fund managers, etc. are not responsible for when cash flows are added or withdrawn from a fund.
Annualized Return
Adding or multiplying all the quarterly returns can give the annual measure of return. For example, if the returns in the first, second, third, and fourth quarters of a given year are denoted r1, r2, r3, and r4, respectively, then the annual return can be calculated by adding the four figures:
Annual return=r1+r2+r3+r4
In practice, the annual return should be calculated by adding 1 to each quarterly return, then multiplying the four figures, and finally subtracting 1 from the resulting product:
Annual return=[(1+r1)(1+r2)(1+r3)(1+r4)]−1
This return is more accurate because it reflects the value that one dollar would have at the end of the year if it were invested at the beginning of the year and grew with compounding at the rate of r1 for the first quarter, r2 for the second quarter, r3 for the third quarter, and r4 for the fourth quarter. That is, it assumes reinvestment of both the dollar and any earnings at the end of each quarter.
This is the preferred method for CFP Professionals and industry standards.
Performance of Pooled Investment
The performance figures are only useful when compared to relevant data. Relevant data include:
Historic Data - to identify trends and averages
Performance of Index - to compare performance against a benchmark
Performance of Competitors - to compare performance against competition
