by WWM | Jul 4, 2017 | Returns
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.
by WWM | Jun 28, 2017 | Returns
In Common Investment Returns we reviewed a few basic measures of returns.
In Assessing Investment Returns we looked at having to analyze returns within proper context.
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.
by WWM | Jun 21, 2017 | Returns
In our first look at investment returns, we reviewed a few common return calculations.
If you know the formulas, the calculations are quite simple. But the key is to understand what is included and excluded between the different returns. That allows for apples to apples comparison when analyzing returns.
But even in standardizing quantified calculations, investment returns can mean different things to different investors.
Today we will consider some of the qualitative aspects in evaluating investment returns.
Return, like risk, is in the eye of the beholder. Never be seduced simply by the quantitative side of investment returns. Always look at results from other angles as well.
I think this is just as important as the hard numbers. Unfortunately, it is an area many investors ignore to varying degrees.
Do so at your own peril.
Expected Rate of Return
Before we get into today’s session, I quickly want to review a topic we have previously discussed.
Expected return is the anticipated asset performance for the future period under consideration.
There are a variety of ways to calculate expected returns and most incorporate multiple variables.
Historic returns, probability and scenario analysis, company specific expectations, general market and industry specific expectations, risks, risk-free returns, etc. There are many factors that go into determining an asset’s expected return.
Because these returns are expected, there is a probability that the actual results will differ.
This is where our earlier discussions of standard deviations come into play. The larger the standard deviation (i.e. the greater the volatility of the asset), the less likely that the actual return will equal the expected return.
As the level of risk lessens, the certainty of the result rises. It is only in investments that have no risk that the expected return will always match the actual nominal return.
In our analysis below, we shall use this simple example.
You invest $1000 in an asset on January 1. You sell the asset December 31 for $1250. There were no cash flows so your total return (also, in this example, your holding period and annual returns) is $250 or 25%.
Nominal Rate of Return
While expected returns are forward looking, nominal returns reflect what actually occurred.
This is the most common way to express a return.
The nominal return is the investment return unadjusted for any other factors. In our example, the nominal return is 25%.
25% return in one year sounds great! Does it to you? Sure it does.
Let’s not be so hasty. There are a few more paragraphs on the page to read.
Nominal return is a good number to know. But on its own, there is no context.
We always need context. Well, at least those who want to properly invest do.
How do we put nominal returns in context? You need to use comparative data.
Real Rate of Return
The real rate of return adjusts the nominal return to eliminate any impact from inflation.
We discussed the affect of inflation previously.
Let’s say that your investment above was made in the United States where the annual inflation rate is running at 3%. Your real rate of return therefore is only 22% (25% nominal minus 3% inflation).
Not too significant an impact. An American attaining that return is likely smiling.
However, perhaps you live in Argentina where inflation is about 27% annually. Your real return becomes a loss of 2%. Even though you made a 25% profit (on which you will be taxed, so your net will be much less), you have actually lost 2% in purchasing power over the year.
For an Argentine, is 25% nominal return good? Not when actual purchasing power erodes that return to nothing.
Or we could consider Venezuela where inflation hit 800% and experts are predicting 1600% in mid 2017. Suddenly, a mere 25% gain will not even help you buy toilet paper (assuming you can even find any in Venezuela currently).
A Venezuelan achieving a 25% return will not be happy at all.
You need always consider the impact of inflation on your returns. Its impact on your real returns can be substantial. And depending on the inflation rate, may make a potentially nice nominal return much less attractive.
Risk-Free Rate of Return
The risk-free rate of return is the return on an investment that carries no risk.
That is, the outcome or return is known with 100% certainty. If the expected return is 10% or $100, you are fully guaranteed the result.
While it is debatable as to whether any investment can be termed risk-free, for investment purposes certain government short term debt issues are considered to be certain. In the United States, the 13 week US Treasury Bill (T-bill) is considered to be a risk-free investment at this time. Similar applies in Canada.
Why is knowing the risk-free rate of return important?
It is believed that investors are rational creatures. That means that all else equal, investors will choose the more efficient investment option when faced with two choices.
Efficiency, in this case, refers to the relationship between risk and return. When having a choice between two investments of identical risk, investors will always select the asset with the higher expected return. Alternatively, when choosing between two investments with identical expected returns, investors will choose the asset with the lesser risk.
While not always followed in practice, it should make sense.
For example, say 13 week US T-bills offer an effective, annual return of 10%. In essence, the risk-free rate is also 10%. That means you could invest in T-bills and be guaranteed a nominal annual return of exactly 10%.
Since all other investments have a higher level of risk, rational investors will never accept less than a 10% expected return for a risky investment.
The greater the risk, the higher the return demanded by the investor.
US government bonds are less risky than most corporate bonds. Therefore, if you look up yields on different bonds, you will see higher yields on corporate versus US government bonds with the same characteristics.
Similarly, riskier companies must pay higher interest rates than more secure companies.
This is the same as personal loans from your bank. If you are a valued client with lots of assets, you might get a loan at the prime interest rate. But if you have no track record of repayment or have had difficulties making debt payments in the past, you will need to pay higher rates than prime.
Use the risk-free rate of return as a minimum benchmark when considering investment options.
If the risk-free rate is 10% and you are contemplating an investment with an expected return of 6% and a standard deviation of 4%, you would never invest in the riskier asset as it offers less expected return.
But what about an asset with a 15% return and standard deviation of 10%? You might give pause. Yes, the potential return is higher than US T-bills, but the risk is significantly higher. In fact, 95% of the time, your actual return will be anywhere between 35% (good) and -5% (not so good).
Whether you think this is a better investment than the T-bills is based on your own risk tolerance. Risk tolerant investors may be enticed with the potential for up to 35% returns. Substantially more than the 10% guaranteed T-bill return. The risk averse may not want to chance losing up to 5%. For them, T-bills are a much preferable and safer investment.
There is no correct answer here. A lot is based on your risk tolerance, investment objectives, and personal constraints.
But by knowing the risk-free rate, you have additional information to make better decisions.
I will say though that I have no idea if an investment with an expected return of 15% and a standard deviation of 10% is good or bad. Like nominal returns, maybe it is or maybe it is not. I need more comparative data.
Relative Rate of Return
With the real and risk-free rates of return we considered investment options relative to inflation rates and guaranteed returns respectively. Those should be baseline benchmarks when assessing potential investments.
But you should also compare your investment returns to other benchmarks. These include: prior year results; analyst or company expectations; the market as a whole; the industry in which the asset lies; predetermined benchmarks.
In our example, the nominal return was 25%. A good return for an American with 3% inflation and a 10% risk-free return. But only relative to those two specific benchmarks.
In reality, I have no idea if it is good or bad return. I need more information.
Perhaps the investment in our example was Fantasy Bank shares.
I would be interested in how the shares performed over the previous years. If the 5 year average return was 40%, maybe 25% this year is relatively weak. Had you bought expecting a 40% return based on historic performance, you will not be happy with a mere 25% actual return.
What if I told you the general stock market grew 12% over the year and that the average banking industry shares rose 30%. You would be happy that your stock outperformed the general market return, but unhappy that you underperformed other banking stocks. On a relative basis, you would have been much wiser investing in a different bank.
In examining potential assets, you consider expected returns. For many investments, analysts and industry experts have expectations for the coming year. If analysts predicted that Fantasy would grow by 50%, you would be disappointed with 25%. Especially if you based your investment on a risk-return profile incorporating the 50% expected return.
You can set up a variety of other benchmarks to compare performance. But you should always compare your actual and expected returns relative to predetermined criteria.
That gives you a few thoughts as to why you should never consider investment returns in isolation.
Always compare your actual and expected returns agains relevant benchmarks.
Your decision-making and portfolio performance will benefit.
Next in our investment series, some further evidence that all returns are not the same.
by WWM | Jun 15, 2017 | Returns
Today we begin exploring the concept of investment returns. A relatively straightforward concept.
The return is the gain or loss you experience on an investment. Pretty easy compared to our risk analysis.
Or is it?
While the above definition applies, investment returns are slightly more complex.
There are a variety of return calculations. The importance of each depends on the individual investor’s personality and circumstances. We will look at three common return calculations today.
Total Return
Total Return equals:
(Sale Proceeds – Purchase Price + Net Cash Flows + Reinvestment Income)/Purchase Price
Sale proceeds and purchase price are self-explanatory.
Net cash flows include interest and dividend income. It may include interest expense on any debt used to finance the investment. And taxes payable on any gains or income incurred.
Transaction costs are sometimes factored into net cash flows. I prefer to add them to the purchase price and deduct them from the sale proceeds. Alternatively, you can track them separately as investment expenses should you so desire.
Reinvestment Income
Reinvestment income is the income you earn on income received. Incremental income earned on reinvested income is a key to compound returns.
For example, you purchase one share of ABC for $10. You receive a dividend of $1.00. You put that cash dividend receipt into your personal savings account and earn $0.10 in interest. You then sell the share for $12.
Total Return is the capital gain (sale proceeds minus purchase price), the dividend income (net cash flow), and the interest income earned from the cash dividend (reinvestment income). In this example, it is $3.10 or 31%.
When calculating, investors often forget to factor in the reinvestment income.
Contextualize Total Returns
31% sounds like an excellent return on ABC. But is it?
Total Return relates to the return over the entire period of time you owned the asset. One day, one year, one century.
Perhaps you bought and sold the stock in one week. Then the return might be impressive (or maybe not as we shall discuss later). But what if you bought the stock in 1970 and sold it in 2010? On an annual basis, 31% over 40 years may not be that attractive.
Or what if I offered you two investments. One provides a Total Return of 100%. The other, 10%. You would obviously be tempted by the first. However, if the holding period for option one is five years and only five weeks for option two, your decision might change.
That is a big problem when people speak of Total Returns. Without any context of time, it is hard to assess the relevance of total return as a performance measurement.
So when someone talks to you about returns, make sure you put it in a time context.
Annual Return
Annual return calculations are very common to equalize and compare performance.
A simple way to calculate Annual Return is to modify the Total Return calculation,
Annual Return equals:
(End Year Value – Start Year Value + Year’s Net Cash Flow + Year’s Reinvestment Income)/Start Year Value
This formula acts as if you bought the investment at the start of the fiscal year and sold it at year’s end.
In using this formula, you can quickly compare performance of different investments over the same time horizon.
Holding Period Return
You may also come across something called a Holding Period Return.
Holding Period Return equals:
(Ending Value/Beginning Value) – 1.
This is like the Total Return except it does not include net cash flows nor reinvested income.
If you invest in assets with significant cash flow aspects (e.g. bonds, preferred shares), you will be missing out on a material portion of actual return by ignoring cash flow and reinvested income.
But if you invest in common shares of small capitalized (“small cap”) growth stocks you likely will not receive any dividend income. In this case, Holding Period Return will equal Total Return.
You can calculate Holding Period Return for any combination of time periods. Just determine a beginning and end date and you are set.
A Lesson to Remember
There are other returns that you will see. We may consider a few more in due course.
If you learn the equations, or have a decent financial calculator, calculating investment returns is not difficult.
But always remember to compare apples to apples and oranges to oranges when calculating and analyzing returns.
Depending on the asset and conditions, different return calculations can yield materially different results.
Make certain that you use the correct ones to arrive at the best conclusions.
And if someone tells you the expected or historic returns are 15% (for example), make sure you know exactly which type of return they are using. This can be an issue with funds. Make sure the performance is net of expenses and fees and not gross returns.
With a variety of return options, you will usually be informed of the one that is most favourable to the person telling you. And that may not be in your best interest.
by WWM | Jun 7, 2017 | Diversification
Today we shall look at a few more areas of interest relating to diversification.
In An Introduction to Diversification, we saw that Investopedia recommends holding a “wide variety of investments” to benefit from diversification.
Further, that a diversified portfolio will generate “higher returns and pose a lower risk than any individual investment found within the portfolio”?
Is this true? What does it mean?
A Wide Variety of Investments?
The greater the number of investments in one’s portfolio, the greater the diversification.
This implies that you should have as many investments as possible in your portfolio.
However, the greater the number, the less the impact from any one additional investment.
If you have a single asset portfolio and add a second asset to the mix, there will be significant impact from the new asset. But if you have 1000 assets equally in your portfolio, the addition of one more will have minimal influence.
The “Ideal” Number of Investments
So what is the ideal number?
The optimal number of individual investments, excluding such things as funds, fluctuates slightly from study to study. Some claim that 20-30 proper investments will result in strong diversification. Other studies found that 15-20 stocks can provide adequate diversification to eliminate nonsystematic risk. Some studies even believe that the benefits of diversification are exhausted in portfolios with more than 15 investments.
As to what is the right number, I think it varies depending on the investor. If I got creative, I could probably build a portfolio of 10 or less assets that managed to diversify efficiently. Others might need 40 to properly diversify. It depends on one’s investment objectives, constraints, accumulated wealth, access to markets, economic conditions, etc., etc.
Asset Correlations are Key
The key to effective diversification is the correlation between the investments.
If you are comfortable investing in fine art within your investment portfolio, you may not require many assets to diversify. If you only want to invest in North American based public companies, you will require significantly more assets to diversify.
Regardless of the “right” number, you can see that it is not substantial. And by that, I mean less than 50 individual assets.
Less investments are also better for long term compounding. Buying and selling multiple investments results in transaction costs and potentially taxes payable on any gains. That negates the impact of compound returns.
Another factor to bear in mind is your opportunity cost (the cost of your time). Researching and monitoring 30-50 existing investments, plus potential assets, can require substantial time and energy. Unless your hobby is financial analysis (a fun hobby, I grant you), you probably do not want to spend your free time monitoring investments.
Higher Returns Through Diversification?
I have thought a bit more about the Investopedia statement. It is still inaccurate, but I think I can explain it.
I do not believe that you can get higher returns just by diversifying. As I explained previously, a portfolio’s expected return is simply the weighted average of every component’s expected return.
But diversification does allow the ability to add higher return assets to the portfolio to improve the overall expected return of the portfolio.
Say you have a two asset portfolio. Asset A has an expected return of 10.0% and a standard deviation of 5.0%. Investment B has a 14.0% expected return and a standard deviation of 8.0%. Your portfolio is 50% of each and the correlation between the two assets is 0.70.
Skipping the calculations, click here if you want to see the basic formulas, the portfolio has an expected return of 12.0% and a standard deviation of 6.0%. Note that we have already breached the Investopedia statement that a diversified portfolio will yield higher returns than any individual investments in the portfolio.
But we can get a nice increase in expected returns by adding a high risk investment to the mix. Let us add asset C with an expected return of 50.0%, but a standard deviation of 30.0%. Further the correlation between asset A is 0.60 and 0.90 with asset B.
The ABC portfolio will have an expected return of 24.6%, a huge increase from the 12.0% expected return of an AB portfolio. But again, the higher average is less than the return of asset C on its own.
So while you may be able to increase expected performance in a portfolio, it will never be greater than the return of all individual assets.
What about risk though?
Lower Risk Through Diversification?
As we saw with our correlation calculations, proper diversification will lower portfolio risk. Again, not necessarily lower than all individual assets though.
In our two asset AB portfolio, the standard deviation is 6.0%. Less than asset B’s 8.0% risk but more than asset A’s 5.0%.
Note that by combining two less than perfectly correlated assets, we reduce overall portfolio risk versus a weighted average calculation (in this case, 6.5%) as we calculated with expected return.
Now let us look at adding asset C to the risk calculation.
The standard deviation of ABC portfolio is 13.5%. Now the combined risk is higher than both A and B on their own and even the AB portfolio itself.
Like returns, Investopedia’s statement on lower risk is a tad faulty.
What Should Investopedia Have Stated?
I am not going to hammer Investopedia as they tend to do a good job. However, by keeping things brief and general, at times you do not get the optimal story. True with everyone, including me.
I might have looked at the impact of diversification on portfolio returns and risk.
For a given return level, proper diversification will reduce the portfolio risk.
Or for a given risk level, proper diversification will provide higher returns.
But that is for the portfolio as a whole, not compared to its individual investments.
Adding Assets to Reduce Portfolio Risk
For example, you have a single asset portfolio, asset X. Its expected return is 20.0% and its standard deviation is 10.0%. You like the return but are concerned about the amount of risk. You decide to add another asset in a 50% mix of the two assets and find two potential investments that both have 20.0% expected returns.
Investment Y has a standard deviation of 10.0%, the same as asset X. Asset Y has a 0.20 correlation to X.
Investment Z has a standard deviation of 7.0%, lower than X. Its correlation to X is 0.90.
An XY portfolio will have an expected return of 20.0%. But an XY standard deviation will only be 7.8%.
An XZ portfolio will also have an expected return of 20.0%. But the XZ standard deviation will be 8.3%.
Both portfolios are more efficient than holding asset X alone.
Note that XY is more efficient than XZ even though Y has a higher amount of risk than Z. That is because of the differences in correlations. The lower the inter-asset correlation, the greater the risk reduction impact.
The same may be said for someone wanting to enhance portfolio returns while keeping risk stable.
Adding Assets to Increase Portfolio Returns
You own asset X and are comfortable with portfolio risk of 10.0%. However, you would like to increase your potential returns. Perhaps you find investment option S with an expected return of 28.0%, a standard deviation of 13.0% and a correlation with X of 0.50.
In combining the two assets equally, the expected return of XS has increased to 24.0%, but the standard deviation remains the same at 10.0%.
Again, correlation plays a significant role in risk reduction. Had the correlations been 0.90 rather than 0.50, the standard deviation of XY would be 11.2%. For investment options with high correlations, you would need to accept lower risk-return profiles to equal the risk of X alone.
Okay, I hope that helps clarify diversification.
And I hope you can see how important asset correlations are in achieving proper portfolio diversification. It is so much less about the number of assets in your portfolio and so much more about the correlation between portfolio assets.
If not, do not worry. It is a rather complicated subject. I just want to lay the groundwork now for when we look at asset allocation and portfolio construction strategies.
I think we will move on to a discussion of investment returns next.