3. Investment Planning. 6. Measures of Investment Returns Flashcards
You have spent a considerable amount of time coming up with an investment plan that you think will help you meet your financial goals. You were careful to find the right asset allocation of bonds, stocks, mutual funds and other investments. So what? What did you do it for? How will you know if you have succeeded or failed? We invest to improve our future welfare. The short-term goal is to get good returns on the money invested. Funds invested come from assets already owned, borrowed money, and savings or foregone consumption. However, you must also seriously think about long–term investment goals. Meeting your long-term investment goal is dependent on a number of factors including your investment capital, rate of return, inflation, taxes and time horizon.
The Measures of Investment Returns module, which should take approximately three hours to complete, will introduce various measurements for investment return.
Upon completion of this module, you should be able to:
* Discuss basic return measurements,
* Explain returns on bonds, and
* Discuss the various portfolio performance measurements.
PRACTICE STANDARD 200-2
Obtaining Quantitative Information and Documents
The financial planning practitioner shall obtain sufficient quantitative information and documents about a client relevant to the scope of the engagement before any recommendation is made and/or implemented.
PRACTICE STANDARD 300-1
Analyzing and Evaluating the Client’s Information
A financial planning practitioner shall analyze the information to gain an understanding of the client’s financial situation and then evaluate to what extent the client’s goals, needs and priorities can be met by the client’s resources and current course of action.
Module Overview
Whether it is short-term or long-term investment planning, returns on investments are crucial to investors. The measuring of investment returns is the only rational way for investors to compare the various investment alternatives. The measurement of returns is necessary for investors to assess how well they have done or how well investment managers have done on their behalf. Furthermore, the evaluation of returns plays a large part in estimating future, unknown returns.
So, how does an individual measure investment returns?
This module introduces the various measurements for investment returns: basic return calculations, bond return calculations, various internal rate of return calculations, and portfolio performance measurement.
To ensure that you have a solid understanding of measures of return, the following lessons will be covered in this module:
* * Basic Return Measurements
* * Bond Return Measurements
* * Portfolio Returns
Click here to view an equation sheet that will be needed for this Module’s Lesson Exercises and Module Quiz.
Section 1 - Basic Return Measurements
Imagine you came home from school and your mother asked how you did on your math test. You told her you got a 78. She knows from experience that it translates into a “C”. She also knows what a “C” means relative to an “A”, a “B”, a “D”, and an “F”. As she begins to lecture you about study habits, and so on, you interrupt her by letting her know that there was more. The 78 you received for the test was the second highest score in the class and when the teacher scaled the scores for the whole class, you ended up with an “A”.
When measuring returns of an investment, you can begin with a very simple equation and make some simple conclusions about your performance. As you add to the complexity of the measurement by applying more variables such as time, inflation, and interest rates, you can draw further conclusions about your performance from different perspectives.
Some measurement methods are more appropriate for certain securities. Just as grades could be scrutinized in many ways (the teacher is an easy or hard grader; the exam took place on a hot day and the air conditioners were broken), it is important to apply the measurement method that appropriately addresses the environment of the holding period.
To ensure that you have a solid understanding of basic return measurements, the following topics will be covered in this lesson:
* Holding-Period Return
* Total Return
* After Tax Return
* Real (Inflation Adjusted) Return
Upon completion of this lesson, you should be able to:
* Calculate holding period return,
* Define arithmetic mean,
* Define geometric mean,
* Calculate total return,
* Calculate after tax return, and
* Determine inflation-adjusted real return on investment.
What’s the formula for Holding-Period Return?
Not on formula sheet!
HPR=(PE+D−PB) / PB
Where:
PE = price in the end of the period
PB = price at the beginning of the period
D = any dividend, interest, or cash flow paid.
Holding period is defined as the length of time over which an investor is assumed to invest a given sum of money.
* The holding period return has a major weakness because it does not consider the time or how long it took to earn the return.
* When this procedure is applied, the performance of a security can be measured by comparing the value obtained in this manner at the end of the holding period with the value at the beginning.
* Please note that in the formula below, any coupon (from a bond), interest, dividend, or any other cash flow received from the investment does not assume reinvestment.
* Any reinvestment (like capital gains distributions and dividends from a mutual fund) would be imbedded in the ending value (P1) and the separate addition of theses payments would overstate the return.
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 = 0.35 = 35%
The HPR can easily be asked for a bond. 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%.
Dan purchased a round lot of 100 shares of Dannon stock for $2,000 or $20/share. Two years later, he sold his shares for $32/share. Dan also received dividends of $4/share. What would be the holding period return?
($3,200 + $400 - $2,000) ÷ $2,000 =
0.80 or 80%
When Maura was laid off, she rolled over her 401k into 3 funds in an IRA:
$2,000 in the Growth Fund
$4,000 in the Growth & Income Fund
$2,500 in a Small Company Fund
After 5 years her statement reflected the following balances:
Growth Fund = $2,782
Growth & Income Fund = $5,699
Small Company Fund = $3,127
Which fund has had the best holding period return?
* Growth Fund
* Growth & Income Fund
* Small Company Fund
Growth & Income Fund
* The Growth & Income Fund had the best holding period return.
* Growth & Income Fund = ($5,699 - $4,000) ÷ $4,000 = 0.42, or 42%
* Growth Fund = ($2,782 - $2,000) ÷ $2,000 = 0.39, or 39%
* Small Company Fund = ($3,127 - $2,500) ÷ $2,500 = 0.25, or 25%
What is the formula for Arithmetic Mean?
The arithmetic average rate of return is a summary of a great deal of information and provides a good way to compare the performance of different investments. The arithmetic mean return (AM), an average of historical one-period rates of return, is computed as follows:
AM=a1+a2+a3+…+an / n
where n denotes the terminal time period.
The arithmetic mean of historical annual returns must be measured over a representative sample period. A representative sample might cover one complete business cycle, measured from either peak to peak, or from trough to trough.
For example, 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?
(.2)+(−.1)+(.05)3
= .05 or 5%
Practitioner Advice: Arithmetic mean is less telling because the standard deviation of the period can vary significantly — the price of the investment could have been very volatile during that period. If so, then the return is not reflective of the movement of the investment during that time.
What would Kerry’s geometric return be if her portfolio yielded -20% return in Year 1, 40% return in Year 2, and 20% in Year 3?
* 10.36%
* 13.34%
* 26.33%
* 26.67%
10.36%
Keystrokes (HP 12C)
0.80 ENTER 1.40 x 1.20 x 3 1/x yx 1 -
The calculator returns:
0.10357, which is also expressed as 10.357%
What’s the formula for After Tax Return?
After Tax Return = Total Return (1 - tax bracket)
Taxes can take away from return as well. It is important to consider how much is paid in taxes on investment gains when evaluating how much you have really earned.
For example, if your investments yield long-term capital gains of $1,000, then 15% of the long-term gains, or $150, is due to the IRS as Federal tax on the gains. Depending on the state you live in, there could be an additional amount due for state taxes as well.
Jed was in the 31% tax bracket and his taxable investments had a total return of 45%. What was his after tax return?
* 32.4%
* 45%
* 13.95%
* 31%
* 31.05%
31.05%
* Jed’s after tax return is equal to his taxable return times reciprocal of his tax bracket.
* 45%(1-0.31)=
* 31.05%
What is the formula for Real (Inflation Adjusted) Return?
(1+r)(1+i)−1
Where:
r= rate of return
i= rate of inflation
In times of changing prices, the nominal return (dollars received) on an investment may be a poor indicator of the real return (also known as the real rate) obtained by the investor. This is because part of the additional dollars received from the investment may be needed to recoup the investor’s lost purchasing power due to inflation. As a result, adjustments to the nominal return are needed to remove the effect of inflation in order to determine the real return. Frequently, the consumer price index (CPI) is used for this purpose.
For example, let’s assume the rate of investment return over some time period is 9%. Over that same time persiod, inflation averaged 3%. One could estimate that the inflation adusted rate of return would be 6% (9%-3%). However, it is important to be exact as small differences in return estimates can lead to large differences in dollars over time. If we apply the formula, we will find the actual inflation adjusted rate of return:
(1+.09)(1+.03)−1 = .05825 or 5.83%
While the .17% difference between the estimated and the actual inflation adjusted returns may seem insignificant, when applied to dollars over a long period of time it can lead to big differences.
Section 1 - Basic Return Measurements Summary
One way to look at how well you have done with your portfolio is to look at its return. Calculating return is a simple process of taking the amount of money you started with and comparing it to how much money you have at the end of your investment period. In the investment world, studying the return of an investment is a way to evaluate how well the investment performed historically, as well as how the investment performed in comparison to its peers.
In this lesson, we have covered the following:
* Holding-Period Return is used as a measure for any investment. It specifies a holding period of any length of time, and the result will be a raw number that is not adjusted to take time value of money into account. Averages can be calculated for single periods within the holding period. Arithmetic Mean is an average of historical one-period rates of return. Geometric Mean is the compound average rate of return.
* Total Return is a stated holding period return used by investments such as mutual funds to communicate how they performed in the recent past. Total return is a standard of measurement that can be used to look at a fund’s historic performance, as well as to compare it to similar funds. It is not an indicator of future performance.
* After Tax Return is the return figure net of any tax expenses that may reduce the actual take-home profit of an investment.
* Real (Inflation Adjusted) Return is determined by adjusting the nominal return to remove the effect of inflation. The consumer price index (CPI) is frequently used for this purpose.
PRACTITIONER ADVICE:
Do not chase after returns. They are historical data.
For example, when bonds or bond funds are displaying high total return figures, they are probably accompanied by a decreasing interest rate trend.
If you buy into that return, chances are the interest rates may be heading up soon and your bond or bond fund prices will decrease.
A diversified portfolio is the best way to avoid chasing returns.
Determining Return:
Determine the total return
Calculate the holding period return: HPR=(P1+D-P0)/P0
Determine the after tax return
Net the tax effect: After Tax Return=Total Return)1-tax bracket)
Determine the real return
Net the effects in inflation: real rate= (1+Nominal Return)/(1+ Inflation) − 1
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)?
* 43.85%
* 36.35%
* 24.54%
* 15.5%
43.85%
* 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 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? (Select all that apply)
* Assuming that the fund’s interest is not reinvested, the price at the end of the year was lower than the beginning
* The fund did not pay any interest because it had a negative return
* The fund paid 2% interest
* The interest was assumed to have been reinvested
Assuming that the fund’s interest is not reinvested, the price at the end of the year was lower than the beginning
The interest was assumed to have been reinvested
* 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 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?
* 4%
* 15%
* 12%
* 9%
9%
* 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%
