In episode 9 on the Wilson Wealth Management YouTube channel, we look at how to compare different investment returns. With so many return calculations available, what are the differences between measures? Which investment returns provide the best information for investor analysis?
How do gross returns compare with net returns? Realized versus unrealized? Base versus local currency?
Why is it important to differentiate?
What is the difference between arithmetic mean and median returns? When should each be utilized in analysis? What are the advantages and disadvantages of each measure?
Can geometric (time weighted) or dollar weighted (internal rate) mean calculations address the limitations of arithmetic mean? Thereby helping investors make better decisions.
What investment return time periods are commonly presented to investors? Why is it important to differentiate by time when assessing asset performance?
What is the difference between nominal and expected returns? How does investment risk (i.e., standard deviation) play a part in this comparison?
How do I know if my investment performance is good or bad? What other return types are there to assist in evaluating my investment results?
When analyzing investment performance, it is important to understand the differences between the various calculations. Especially as the preparer will undoubtably choose the ones most favourable to his/her perspective, not yours.
Today we review and differentiate two additional investment return calculations: geometric mean or time weighted return and the dollar weighted or internal rate of return.
A tad more complicated. But much more helpful with your performance analysis.
Geometric Mean (Time Weighted) Return
The geometric mean is also known as the time weighted rate of return.
It measures the compound growth rate of the portfolio’s beginning market value over the evaluation period. The geometric mean return assumes that all cash flows are reinvested in the portfolio.
To calculate the geometric mean you need to add 1 to each period’s return. Then, multiply the results together for each period. Next, take the root value using a root equal to the number of periods. Finally, subtract 1 and you get the result.
Not as easy a calculation as the arithmetic mean return, but not too complex.
In my prior post’s arithmetic mean example, we had three year returns of 10%, 20%, 5%. The arithmetic mean is 5%.
The geometric mean return though is = [(1-0.1)(1+.20)(1+0.05)]1/3-1.0 = 4.3%
Note that the geometric mean is always less than the arithmetic mean. Good to know for quick calculation checks.
In our second arithmetic example, we had two periods with results of 100% and -50%. Year one we went from $1000 to 2000. Year two, we fell from the $2000 back to our original $1000. Ended up right back where we began, so our actual return was $0 and 0%. Yet our arithmetic return is 25% ((100-50)/2).
This makes no sense. Enter geometric or (hint hint) time weighted mean returns.
In looking at the geometric return, we see that this is addresses the illogical arithmetic result.
The geometric mean return = [(1+1.00)(1-0.50)]1/2-1.0 = 0%
This calculation reflects the reality of how returns are impacted by prior periods’ accumulated results.
Unless you need to know the calculations for exams, I suggest you not worry too much about them.
The key is to know that arithmetic mean returns are useful for independent data, whereas geometric mean returns are best used for investment results where the data is interdependent to some degree.
Also, when comparing arithmetic to geometric returns, arithmetic results will always be higher for identical data.
Dollar Weighted (Internal Rate of) Return
You may see comparisons between time weighted (geometric) and dollar weighted returns (internal rate of return).
Dollar weighted returns calculate the interest rate that equates the present value of the cash flows from all investment periods under consideration plus the end portfolio market value to the portfolio’s beginning market value.
In essence, it is the internal rate of return for the portfolio.
For example, on January 1, 2015 you invest $1000 in a 1 year term deposit earning 10% interest. On January 1, 2016 you reinvest the proceeds of $1000 into another 1 year term deposit earning 15%. You also invest an additional $2000 into the same term deposit. On December 31, 2016 you receive $3565 in cash.
Going through the manual calculations starts to get tricky here. Fortunately there are many good financial calculators that do the work. Or, if simply analyzing data, returns are often provided in different forms.
As for our example, by plugging the data into my handy HP 12C we get a return of 13.66%.
Dollar weighted returns provide useful information as to growth of a portfolio.
However, dollar weighted measures are not usually very useful in evaluating portfolio performance. That is because the return is affected by events outside the control of the portfolio manager.
Changes in funding, such as client contributions or withdrawals, will impact the dollar weighted return. This makes it difficult to compare the performance of two managers over time.
When evaluating two separate funds in which you wish to invest, do not put too much emphasis on the dollar weighted returns in your comparison.
That concludes our initial look at investment returns.
Next up, we will consider how risk and return relate to investor profiles.
We will review three common investment returns that are useful to understand and differentiate in analyzing performance.
Today we cover arithmetic mean investment returns. This is the most common measure and one that you use in daily life.
We will also compare mean versus median returns. Median being a term you may also encounter.
Next post will cover the other two important return calculations; geometric and dollar weighted average returns.
Mean versus Median Returns
The mean is the average of all the individual data points.
The mean is not the median, another term you may encounter.
The median return is simply the physical mid-point for all the individual results.
For example, you have 5 years of investment results: 10, 5, 22, 12, 11.
The arithmetic mean is the average of all results. Add the results and divide by number of years. In this case, 12.
To calculate median, you must rearrange all the data points from lowest to highest. Then find the exact mid-point.
In this example, we re-list the data in ascending order as: 5, 10, 11, 12, 22. The number at the mid-point is 11. That is the median. Do not forget to place the data in ascending order regardless of time period incurred.
Median Usefulness
The median is useful in letting you know that half the results are above 11 and half are below.
Medians are less sensitive to extreme scores (ie., outliers), so may be a better indicator for smaller sample sizes. Means can be impacted by a few extreme results, so provide better information in larger sample sizes.
In our example above, let us change the one data point from 22 to 220. The mean changes from 12 to 51.6. While it is indeed the arithmetic average, when compared to the other numbers in the sample, it appears unusual.
Does it really represent the “average” result from that time period?
If a mutual fund salesman tells you that his fund has averaged 51.6% over 5 years, you may expect that to be indicative of next year’s return. In reality, four of the five prior years had returns equal to or below 12%. Which do you think is more likely next year?
However, the median still remains at 11. The outlier had no effect on the median. If the fund salesman told you his fund had a median return of 11% over the five years, that is more representative of the prior years’ results.
However, if you are a fund salesman, what closes the sale better? Telling a potential investor that the 5 year average return is 51.6% or that the median return over that period is only 11%? I shall wait while you ponder this toughie!
Median Not Great in Real World Investing
That said, other than its relevance for small sample sizes and extreme results, I find the median of little real use in investing. But as you can see from the above example, knowing both the median and mean averages can provide better overall context.
Despite the potential impact of outliers, mean return can be quite useful in investing. Knowing the average results over a period of time or other criteria is important to the decision-making process.
There are a variety of mean calculations. Depending on the formula employed, the average returns can differ significantly.
Further, certain mean returns are good for some calculations, but are less relevant for others.
Arithmetic Mean Return
In our example above, I used the arithmetic mean calculation.
An arithmetic mean return is simply the sum of all the returns divided by the number of returns.
For example, you are analyzing an investment whose returns over the last three years were -10%, 20%, and 5%.
The arithmetic average return is 5% = [(-10+20+5)/3].
Pretty simple. Something you often calculate in everyday life.
Good for Independent Returns
Arithmetic mean returns are useful when data in the series is independent from each other.
For example, the arithmetic mean is relevant when calculating the average exam results for a class of students. The performance of each student is independent of the others (assuming no one is cheating by copying another student’s answers!). How you score is not affected by the students sitting around you.
Or when measuring the mean height of all the students in your class. The height of the student on your right should have no impact as to your own height.
But Investment Performance is Inter-Dependent
However, in investing, performance between periods is inter-related.
For example, if you invest $1000 and earn 100% in the first year, you start year two with $2000 in capital. But if you lost 50% in year one, you would only have $500 in capital at the beginning of year two.
In year two, let us say that you had a 20% return. In one scenario, your $2000 would grow to $2400. However, under the second scenario, your $500 would only grow to $600.
Same percentage gain of 20%, but significantly different monetary change.
You can see how the cumulative investment performance is inter-related to past results.
Negative Returns and Arithmetic Returns
A problem with using the arithmetic mean return for investment calculations is that negative returns skew average returns and sometimes make the results irrelevant.
For example, you invest $1000 on January 1, 2015. On December 31, the investment is worth $2000 and there were no cash flows during the year. Your annual and holding period return for 2015 is 100%.
You hold the investment throughout 2016 and at December 31, the value has fallen back to $1000, with no cash flows. Your holding period return for 2016 is -50%.
Your arithmetic mean return for the two years is 25% = [(100-50)/2].
But at December 31, 2016 you have exactly what you initially invested on January 1, 2015. Your return is 0%. It did not increase, on average, by 25%.
Always remember that negative returns skew arithmetic mean return calculations.
Also remember that arithmetic mean returns bias the average upwards.
To deal with the shortfalls of arithmetic means is where the geometric mean return becomes important. We will cover both geometric and dollar weighted returns next time.
Today we will see the need to look within the return itself when evaluating true performance.
This is because all investment returns are not created equal.
Gross versus Net Returns
Gross returns are before expenses, transaction costs, management fees, and taxes are deducted to arrive at net return.
Fund and managed portfolio performance may be reported on either a gross or net basis. The trend is to require reporting on a net basis, but there are often variations between countries.
Make sure you know which is reported in your jurisdiction as well as any costs that might be omitted from the performance calculation. Everyone likes to spin their return figures as positive as legally possible.
Investment Costs to Monitor
Various expenses, transaction charges, and management fees are common in mutual and hedge funds, as well as in managed portfolios. When reviewing funds, you can usually ascertain any additional costs to the fund that negatively affects performance.
Key ratios to review are the Management Expense Ratio (MER) and Total Expense Ratio (TER).
We will discuss these costs when we look at mutual funds as an asset class. They vary significantly between funds and can have a great impact on your portfolio growth.
With stocks and bonds, you do not need to worry about management fees.
Don’t Forget Taxes
Taxes are extremely important when assessing returns. Unfortunately, many investors ignore taxes in their analysis.
Taxes can affect your investment performance in two ways.
First, the investment you own may have taxes deducted at the source. For example, foreign dividends or interest may have taxes withheld by the issuer. In many instances, you may get a foreign tax credit for taxes withheld in another jurisdiction, but not in all cases.
Perhaps you own preferred shares paying out 10% annually. If the dividend withholding tax is 25% and there is no treaty allowing you a foreign tax credit, you only receive an actual return of 7.5%.
Had you factored in the foreign tax effect when selecting the asset initially, it may have made the investment unattractive.
Second, in most countries, taxes are payable on passive investment income or capital gains earned on investments. You need to factor in the tax payments as part of your overall portfolio performance.
If you earn 10% in interest income, your gross return is 10%. But if you must pay 40% of that amount in taxes, your net return falls to 6%.
Different Tax Rates Impact Investment Decisions
Earnings from interest, dividends, and capital gains are often differentiated by governments and taxed at varying rates.
For example, in Canada, interest income is taxed at the highest rate for all investment income.
Capital gains are included in income at only 50% of the gain. This causes the effective tax rate on capital gains to be less than for interest income. Additionally, capital losses may be carried forward or back for a number of years to offset other capital gains.
Dividends from eligible corporations receive dividend tax credits that reduce their effective tax rate. Whereas dividend income from non-eligible corporations do not generate a dividend tax credit.
Whichever form you generate your income stream will have implications for taxes payable and your net returns. This can be incredibly important when analyzing and selecting potential investments.
Perhaps you have two Canadian investment options. One offers an annual interest payment of 15%. The other offers a guaranteed capital gain of 12%. If you only consider the gross returns you should take the interest stream.
But if you factor in that capital gains in Canada are only included in income at 50% of the gain, the numbers change. If you are in a 40% tax bracket, you would have a net return of 9% on the interest. Whereas the capital gain would have a net return of 9.6%. An improvement over the interest only investment.
Also, in many jurisdictions, tax is payable when the income is considered earned, not necessarily when it is physically received. We will see how this works below.
Realized versus Unrealized Returns
Realized returns are those where you have received the cash. You receive a dividend or interest. You sell an investment.
Unrealized returns are those that are only on paper.
This can be a tricky area. In my mind, investment gains are not real until the cash is in my jeans.
Unrealized Gains and the Housing Bubble
I believe that unrealized gains contributed to the housing bubble in many parts of North America. Initially, when someone buys a house they usually take out a mortgage. Banks typically lend between 75-95% of the appraised value.
When house prices were rising many individuals had their homes re-appraised at higher levels than when they bought the house. With this extra equity, people took out home equity loans for a variety of purposes.
As the housing market substantially slumped and values fell, these individuals often found themselves with more home debt than the house was actually worth. Faced with greater debt than value, some just walked away from their homes.
When assessing investment performance, it is fine to consider unrealized returns as well as realized ones. However, make sure that you do not count the proverbial chickens before they hatch.
Until your investment is actually sold and the proceeds are in your bank account, much can happen to the asset value. Often, negatively. Do not spend your gains before you really have them.
More Tax Considerations
A second concern with unrealized returns relates to taxes.
At times, interest or dividend income may be accrued but not paid out by the investment.
For example, a dividend is declared in November and payable as at December 20. You physically receive the dividend distribution on January 15. At December 31, you have yet to receive the dividend, but the income is considered accrued.
In many jurisdictions, the tax authorities treat accrued income the same as if you had actually received it.
If you do not want to pay tax on returns not yet fully realized, be careful with the timing of the payment stream of your asset. In some cases, especially with accrued interest income, the impact from taxes is harsh.
As I often recommend dividend or interest reinvestment plans to aid in generating compound returns, you must be careful here. You will “receive” the income, but as it is immediately rolled back into the investment, there is not associated cash in the bank. However, you are still expected to pay the tax due on the income. Keep this in mind when reinvesting income.
Base versus Local Currency Returns
We looked at the difference between base and local currencies in our review of systematic risk.
Always be careful when dealing in multiple currencies. It is crucial that you compare foreign currency returns to the currency you use in everyday life.
That gives you three common variations between investment return calculations.
We will look at three different examples of mean investment returns in our next entry.