Problems With Price-Earnings Ratios

The price-earnings (P/E) ratio is probably the most widespread analytical calculation used by investors.

Yes, it can provide insight into a company’s share price. Note that I say can, not does.

But there are also a few potential problems with P/E ratios.

Garbage In – Garbage Out

Calculations are only as good as the quality of inputs.

If it were easy to estimate future earnings and price-earning multiples, one could accurately chart future share price. Then analysts would be at home getting rich, not crunching numbers all day in a tiny office or cubicle.

There are so many variables that need to be factored into a company’s future earnings that it is impossible to get them all right, or even close to right.

And there are always unforeseen events that take place to complicate things further. Even if your data is pristine and not garbage, you still run the risk of getting it wrong.

On September 10, 2001, I do not imagine many analysts factored in the next day’s terrorist attacks that impacted share prices across the board.

In 2016, how many analysts foresaw the Trump election in the United States? Not that this is directly correlated to the yuugge increase in equities in 2017, but there was some impact. Not to mention all the “experts” who claimed that stocks would tumble if Trump was elected.

In late 2017, tax reform legislation was passed in the United States. Again, this was unforeseen a year prior and will have direct impact on many U.S. based companies. As well, if you follow international news, there is concern in many countries that U.S. based companies may now have competitive advantages over (say) German or Australian firms. This has led to calls of similar corporate tax reform in these jurisdictions to level the playing field.

So many examples out there of how consensus views suddenly had to adjust. In 2018 and beyond, this will also be true.

Both the number of variables and the possibility of unforeseen events occurring makes it very tough to accurately estimate EPS. And the farther away the estimate, the greater the probability of error.

When relying on someone’s estimates, never take them as the absolute truth. Inputs may be good at that moment in time, but may become irrelevant in the near future.

Data is Fluid

The data impacting future earnings is always changing. Similar to my above examples, these occur at the company level.

Each day new information is uncovered that affects a company’s future performance. The departure of a key executive, the announcement of a new contract for sales to China, a lawsuit against the company, a new product, etc.

With each piece of new data, the expected future results will change. As such, both future expected EPS and P/E for a company may be fluid and shift up and down over time.

No One Sees Things the Same

Different analysts may arrive at completely different conclusions, even given the same facts.

For example, consider JPMorgan Chase. A rather large company in the relatively stable finance sector. Not hugely volatile.

Per Yahoo Finance as at January 2, 2018, JPMorgan has 26 analysts estimating its 2018 EPS. The average estimate is USD 7.77. However, the lowest estimate is USD 7.45, while the highest is USD 9.25.

Not a huge variance, but given that all analysts should have access to the same raw data, you would expect a much tighter range. The difference is due to how each analyst interprets each variable.

Even at this level, who is “right” and who is “wrong” can result in different valuations.

As at January 2, JPMorgan traded at USD 107.26 with a 15.46 trailing P/E ratio. If the ratio holds, the consensus opinion is that JPMorgan has a target share price as at December 31, 2018 of USD 120.12. A nice gain of about 12% for 2018.

However, the pessimistic analyst with the USD 7.45 EPS estimate only expects a price of USD 115.18. A gain of only 7.4%. Whereas, the analyst who estimates EPS of USD 9.25 expects a share price of USD 143.00. A gain of 33.3%.

Quite the different outcome for two investment professionals assessing the same raw data.

And that is an established company in a relatively stable industry. If you look at small or new companies, or those in more volatile sectors, you will likely see greater dispersion in estimates.

For example, Facebook (FB). As at January 2, it has 41 analysts predicting 2018 EPS of USD 6.63. At today’s share price of USD 180.21 and trailing P/E ratio of 34.88, that leads to an estimated share price of USD 231.25. For a gain of 28.3%. Much better than the consensus 2018 increase of 12% for JPMorgan.

However, the range in 2018 EPS estimates for FB go from USD 5.73 to 7.45. At the high end, that translates to a share price of  USD 259.86 and a gain of 44%. But on the low side, it may mean only a share price of USD 199.86 and a 10.9% increase. At this lower level, JPMorgan might actually be the better (and less risky) investment.

You can see there is quite a range of results depending on how the raw data is interpreted. Who you follow can play a significant role in your investment choices and expectations.

Bitcoin (and other cryptocurrencies) is an extreme example of this. At the end of 2015, Bitcoin traded at USD 429.78. By the end of 2016, it was trading at USD 958.24. A gain of 123%. Nice.

Starting 2017, some saw Bitcoin much like Dutch tulips. Others as the wave of the future. But I am not sure very many estimated Bitcoin trading near USD 15,000 at Christmas. Quite the increase.

This is why investors religiously follow specific analysts who have excellent track records. And why these same analysts earn extremely high compensation.

And yes, I am ignoring the herd mentality effect of analysts. Something that is very real and actually works to keep estimate ranges closer than they should be. A few analysts like taking contrarian views. But the mast majority like to hide safely within the herd.

Sometimes All Stocks Are Down

Even strong companies may fall in price.

In a bear (down) market, many stocks appear undervalued. But until the market, as a whole, improves and investors start to invest in equities again, the undervalued stocks may not increase in price.

In fact, they may fall even further.

Just because a good company has a low P/E does not mean it will rise in price anytime soon.

One needs to have patience when value investing.

The same is true in bull markets. Some companies just ride the market wave, resulting in over generous P/Es.

Undervalued or Junk?

Investors value a company’s growth potential in the P/E calculation.

If investors believe the potential for a company is strong, it will have a higher P/E than one whose prospects are weak.

If you focus only on stocks with low P/Es, you may find some undervalued companies. But you may also end up investing in firms whose earnings potential is seen as weaker than in comparative companies.

Separating the value plays from the dogs is always a challenge.

The quantitative analysis may give the same results to two companies. But one may be a value stock, the other a piece of junk. That is why investors should never rely on P/E, or any ratios, on their own. They need to be combined with qualitative analysis.

It is the qualitative, not the quantitative, analysis that separates the good from the bad.

I suggest you never forget that.

Next up, the price-to-book ratio.

Price-Earnings Ratio

In equity analysis, price-earnings is the most common ratio calculation.

Used to analyze most investment styles, it is a cornerstone of value investing.

Today we look at the concept and how to use it. 

Note that the examples below use real data as at December 18, 2017 in US dollars.

Price-Earnings Ratio

Price-earnings (also seen as Price/Earnings or P/E) is a widely used fundamental.

To calculate, simply divide a company’s earnings per share (EPS) into its current share price. That said, most stock ticker services provide P/E ratios in their quotes and financial information. So you normally need not calculate.

For example, Wells Fargo & Company (stock symbol: WFC) is a financial services company that operates primarily in the United States. On December 18, 2017,  WFC traded at $60.99 per share.

WFC has trailing 12 month diluted EPS of $3.87. Therefore, its P/E ratio is 15.76.

Very simple to calculate (or pluck from the Yahoo Finance website).

But is WFC’s P/E ratio good or bad? I have no idea. And sadly, Yahoo Finance does not provide its opinion.

Analysts and investors can never consider data or ratios in isolation. We need to look at comparative data.

Compare a Company Against Itself

That may be the company’s historic or expected future P/E ratios.

Look at Historic Results

How does the current P/E ratio compare with the same company’s over time?

If you knew that the average P/E over the last decade was 11, yet now it is 15.76, that should give pause. Is the stock overvalued? Or perhaps it has added a new product line or market, corporate acquisition, cost cutting measures, etc. Changes that will increase future EPS to bring the P/E back in line.

Conversely, if the historic average P/E for WFC is 20, perhaps the stock is undervalued. Or maybe the lower than historic P/E ratio reflects investor sentiment that trouble is ahead for the bank.

Yet again, it is the qualitative analysis that helps determine potential versus pitfall.

And Future Expectations

While the past is interesting, you need to always focus on the future.

This is true for any analysis, not just the P/E.

WFC current EPS for the trailing 12 months is $3.87. For next year, per Yahoo Finance data, the estimated EPS is $4.32. This results in a Forward P/E ratio of 14.11.

This may be a positive. As the stock price is a constant at December 18, a lower Forward P/E must mean that EPS is expected to increase next year (as it does). Usually, increasing EPS is a good thing.

Compare Against External Measures

As well as comparing a company to its past performance and futures estimates, you should consider relevant outside measures. Key competitors, it’s industry, and sector of operations. Perhaps even to the market as a whole.

Note: Depending on the market, industry, or specific sector, you may or may not be able to find P/E data in aggregate. If index data is not available, a useful little trick is to substitute comparable mutual or exchange traded index funds. Funds typically provide P/E (and/or other) ratios paralleling their tracked indices in the performance data.

With WFC, let us compare its P/E against the market as a whole. Then its industry and key competitors.

Compare to Broad Market

Try to find a broad market that is relevant to your stock.

WFC operates, and is listed, primarily in the U.S. It makes more sense to compare WFC ratios to a broad U.S. index than Hong Kong’s Hang Seng or Germany’s DAX.

WFC is a significant component of the S&P 500, a broad U.S. market index. Currently, WFC is the 12th largest component of the S&P 500, representing about 1.17% of the index. That should be an appropriate benchmark.

If we have index data, we can compare directly to the index. And the S&P 500 data is often available to retail investors.

But let us assume, for demonstration purposes, we cannot get direct index data. We can compare WFC to (say) the iShares Core S&P 500 ETF (symbol: IVV) as it reflects the market index closely. IVV trades at a P/E of 23.77 versus WFC P/E of 15.76 as at December 18.

Note that in comparison the actual S&P 500 trades about 25 currently, with slight variances between reporting companies due to measurement dates.

A lower than market P/E ratio may indicate WFC is undervalued. If WFC traded at the average 23.77 market multiple, you would expect a share price near $91.99 ($3.87 EPS * 23.77). As it trades at $60.99, there is potential for appreciation.

However, WFC is a financial services company. Relative stable and lower risk (with lower expected returns) than other components of the S&P 500. For example, the more volatile Information Technology sector makes up 24% of the index, whereas the less risky Financials are 14%. I am not sure a bank should trade at the same premium as Apple or Facebook.

While comparing P/E of a company to the market as a whole is fine, it can become a bit of an apples an oranges analysis. Probably better to drill down to where we can (hopefully) compare apples to apples.

Drill Down to Industry P/E

Let us compare WFC to iShares U.S. Financial Services ETF (symbol: IYG), a sector index fund. As the name indicates, its focus is more on companies such as WFC. In fact, WFC is the fund’s third largest holding at 8.64% of total assets.

The P/E ratio for IYG is 20.32 versus WFC’s 15.76. That too indicates room for price appreciation in WFC. However, just be careful. Even though we are comparing WFC against companies in the same industry, we must consider size and stability.

WFC is a relatively large company in the sector. As we saw above, the fund’s third largest holding. That means there are plenty of smaller, less stable, financial services companies in the index. These companies are typically riskier, so investors demand higher P/E multiples. While we drill down to the industry, probably prudent to also compare WFC to its true peers.

And Direct Competitors

The top five holdings in IYG are: JPMorgan Chase (symbol: JPM) at 11.87%; Bank of America (BAC) at 9.15%; WFC at 8.64%; Visa (V) at 6.59%; Citigroup (C) at 6.40%. If we exclude Visa, the remaining banks are comparable.

As at December 18, each bank has the following P/E ratio: JPM 15.39; BAC 16.89; WFC 15.76, C 14.53. At this level, the market is pretty efficient and all companies trade at similar multiples.

As you perform your qualitative analysis, you will determine if WFC should be trading at the same (or higher) multiple than BAC. If so, based on earnings of $3.87, you might buy WFC in the expectation that its price will rise to equilibrium with BAC’s P/E and trade at $65.36. An increase from where it sits now at $60.99.

Or you may assess that it ranks on par with C at a 14.53 P/E. If so, you may expect a price decline in WFC to $56.23.

Not the easiest task in the world to determine whether a stock is a buy or sell from its P/E ratio.

The data is actually of more use than you may think after reading the preceding on WFC. However, as with all investment analysis, it is the qualitative side that brings clarity to the quantitative calculations. And that qualitative expertise comes with time and experience.

Next up, we will consider some additional potential problems with P/E ratios.

 

Quantitative & Qualitative Analysis

Before we look at the next investment style debate, I want to go through the two types of fundamental analysis.

You will encounter both quantitative and qualitative analysis (aka “Quants & Quals”) when researching potential investments. Both are important to understand, as well as knowing their strengths and weaknesses.

Quantitative Analysis

Quantitative analysis looks at hard data. That may be the economy, market, industry, company, etc. You may also see this called the “fundamentals”.

A company’s fundamentals are compared to historic results and expected future performance. A company is compared against fundamentals of its peers, the industry and sector in which it operates, and the stock market as a whole.

Common fundamentals include: price/earnings; price/book; dividend yields. We will look at each in separate posts.

It is relatively easy to perform quantitative analysis.

Find the correct data – not always a simple thing to do, especially for small companies -, plug it into the appropriate equation, and you have your result.

But if it were that easy we would all be very wealthy.

Qualitative Analysis

Investors tend to do a decent job on quantitative analysis. That is, most arrive at similar ratios and results.

What usually trips them up is the qualitative side.

I believe qualitative analysis is the key to any investing decisions. Whether they be stocks, buying a home, or lending money to a friend. So pay close attention to this side of analysis when researching any potential investment.

Based on quantitative data, terrible investments may look attractive. No one wants shares in bad companies. Weak demand and excess supply drive the share price of a junk company lower. Unfortunately, the fundamentals (being a function of the share price) tend to look very good, when instead they should be a warning to potential investors.

When we cover the common fundamentals later, we will go through some examples.

Qualitative analysis uses non-numeric data to assist in separating the wheat from the chaff. It provides context to the hard number quantitative analysis.

Qualitative analysis involves assessing a company’s nonsystematic risks (see Part I and Part II for greater detail), including: management; operations; competitors and the industry.

Management

Management is the number one driver when I consider companies.

Equally important when assessing mutual or exchange traded funds. Strong fund management is crucial.

Management makes the decisions that impact operating performance and ultimately the share price. As an investor, you want to invest in well-run companies. If you do, you will increase your probability of positive returns.

Who is on the management team?

Review their credentials and experience in the industry. What is their track record of success?

With key management, past performance is an indicator of future results. Both good and bad.

How long has the current management team been in place?

If a successful company has recently lost key management, it may be a sign of problems or changes in the approach to running the company.

If management is new, were they successful in their previous ventures?

These are some of the questions you should consider.

Operations

What does the company do? Does the business model make sense in today’s world?

A few years ago, manufacturers of floppy disks were profitable. Today, if they have not evolved into making flash drives or “in-the-cloud”, they are no longer in business.

What is your experience with the company’s product?

Consider something as simple as cola products. Let’s pretend that Coke, Pepsi, and RC Cola are all separate companies with only one product, cola.

When you are at the grocery store, in a restaurant, or at an event, what do you see? A lot of Coke and Pepsi for sale, but much less for RC. Intuitively, who do you think sells more cola?

When you plan to invest in a company, think about how its products are seen in the world.

The same is true for your personal likes and dislikes.

For the most part, you are the “average” consumer. Trust your judgement when investing.

Maybe you plan to buy a smartphone and options include iPhones, Blackberries, and Androids.

Which one is getting the best reviews? Which one did you purchase or would like to buy? What are your friends buying?

If you are a typical consumer, then there is a high probability that other consumers are making the same choices as you and your friends. This results in stronger sales than competitors, which should enhance profitability and the share price.

When assessing a particular company, always consider its products. If the product is junk, there is a good chance that the stock is also junk and not a good investment.

That said, a lower end company may be undervalued and a good buy. Or well regarded companies may be overpriced and not great investments. You want to invest in good companies. Just not at too big a premium.

Industry and Competitors

Just because your quantitative analysis indicates a stock has potential value does not mean it is a great investment.

If the industry is in a downturn, even good investments may suffer.

Consider the real estate market. Perhaps it is in a major slump in your region. If you intend to sell your home, you may have to accept less than you believe to be its true value. It is not the fault of the house, rather it is an industry wide issue.

Often you will find a well-managed company that sells quality products. But in their market segment, they cannot compete against even stronger competitors.

Apple came to dominate the MP3 player market with its iPod, then iPhone. Even competitors with good products suffered.

You may love a product, but always review it in light of the industry before investing.

This is obviously not an exhaustive list of things to analyze.

Legal issues are often key. Government policies – regulatory, tax, subsidies – may also need review. Depending on the industry or company, there may be other crucial items to review.

For example, solar companies may only be currently viable due to government subsidies and incentives. Or consider The Weinstein Company. Until recently, a well regarded film studio. After all its legal and related issues have come to light, its value has plummeted.

Market Capitalization Segments

Within investment styles, it is common to aggregate assets by market capitalization.

To find a company’s market capitalization (or “cap”), multiply current share price by number of shares outstanding.

Market capitalization is useful in comparing companies of similar size. Understanding the differences between each size segment is useful. For example, how you analyze large cap stocks will differ from micro cap equities.

Also, stocks in the same segment often respond to similar variables. Global behemoths may be impacted by an earthquake in Japan. Whereas, business tax policies in Canada may be more important to small Canadian based companies.

You will not need to calculate market caps, but you should understand the general differences between cap segments.

So what are the different segments?

Market Capitalization Segments

You will always see three market capitalization segments: large-cap, mid-cap, small-cap.

Less common are three additional categories: mega-cap, micro-cap, nano-cap.

These terms have some flexibility in usage and in ranges for each segment. I will provide the common categories, but be aware that you may see slightly different terminology and different ranges at times.

However, the general concepts are applicable. Big is big, small is small, and how companies operate within their specific market cap will differ versus other caps. Also, external factors impact companies differently depending on market cap.

Segment Ranges

Over $200 billion (US dollars) are the mega-cap companies. Some consider $100 billion the hurdle. Big, big, companies. Normally with a global presence. Microsoft (market capitalization of $491 billion in December 2016), Google ($560 billion), Apple ($616 billion) and Exxon ($384 billion) are examples of these extremely large companies.

Between $10 billion and $200 billion are large-cap. Some use $5 billion as the low end. May be referred to as “big-cap”. If mega-cap is not used by the rater, they are included in the large-cap segment.

$1 billion to $10 billion are mid-cap.

$300 million to $1 billion are small-cap.

$50 million to $300 million are micro-cap.

Below $50 million are nano-cap.

If micro or nano are not utilized, these segments will be part of the small-cap segment.

Ranges May Differ

Raters Use Different Ranges

Some investment professionals, mutual fund companies, or ratings agencies may use different terms and/or ranges for the market segments. Do not become fixated on terms or ranges. Just understand the general breakdown and know that large cap is different from small cap.

Investopedia groups companies between $300 million and $2 billion as part of their small-cap segment.

Morningstar utilizes percentages to segment stocks. Equities are divided into 7 geographic regions. Within each region, the top 40% of stocks are classified as giant-cap. The next 30% are large-cap, the next 20% are mid-cap and the last 10% are deemed small-cap.

With this Morningstar system, internal and external comparisons may be difficult.

Perhaps a stock construed as a large-cap in Latin America is only a mid-cap in the Greater Europe region. This makes internal comparisons of global companies within the Morningstar system harder than by using a fixed dollar calculation.

May Become Apples to Oranges Comparisons

Second, it makes external comparisons between rating organizations difficult. Morningstar has Canada as a unique region, so the bottom 10% of Canadian companies in size are considered small-cap. But unless I know the exact cut-off point, it is hard to compare to someone that uses a threshold of $1 or $2 billion for Canadian firms.

When assessing stocks as large, mid, or small-cap, do not blindly accept the classification by the organization that segments the equity. Do your own analysis to ensure that, in your own mind, you know what type of company it is.

Why is Market Capitalization Important?

Bigger Companies May Be Safer

First, investors often view larger companies as being more stable in nature, less risky, with broad operations that smooth earnings over time. Many large companies are considered “blue chip” investments because of their size, longevity, and the fact that they are a known business. Think Coca-Cola, Google, Nestle, HSBC, etc.

Smaller companies may be seen as riskier. Perhaps due to lack of public awareness, niche markets, lack of longevity, or merely due to a regional presence. Freenet AG (Germany), Coherent Inc. (US), Pigeon Corp (Japan) are small caps. You may not have heard of them, or most other small companies.

This may be how investors view the different market caps. Bigger is safer. Not necessarily true. But bigger and better known may make investors feel safer.

As a result, lower risk investors may prefer larger cap companies. More aggressive may seek out small cap.

Market Caps Fluctuate

Second, market capitalization may fluctuate over time based on how a company’s share price performs, as well as the number of outstanding shares it has. Many small-cap companies aspire to increase their share value so as to move up into mid, or even large-cap, segments.

Many of today’s mega cap companies once began as small cap stocks. In fact, many investors target small companies trying to find the next Apple or Microsoft before they make it big.

Some companies slip over time to lower segments. Being large is not protection from declines in value.

Consider the Canadian telecommunications company, Nortel. Once the darling of Canadian investors. In September 2000, its market capitalization was CAD 398 billion and it employed almost 100,000 staff around the world. A well-known, stable company that easily fit the mega cap segment.

Less than two years later, Nortel was worth under CAD 5 billion. By 2009, shares were trading at CAD 0.19 and the company was delisted.

If you had wanted to invest only in large or mega-cap equities and bought Nortel in 2000, you would have found yourself owning a small-cap stock very quickly. And in a further few years, worthless paper.

What goes up can also come down. Sometimes in a hurry.

Larger Usually Means More Liquidity

Third, the larger the capitalization, the more shares are outstanding, which normally translates into increased liquidity for investors. Liquidity risk is a real issue for investors.

When investing in nano or micro-cap companies, you may find it difficult to buy or sell shares on a timely basis and/or at your target price. This may also be the case for small-cap stocks.

Reduced liquidity can increase the price volatility (risk) of an asset. That is why smaller capitalized companies are generally considered riskier than larger companies. This has little to do with the risk of the company and its business. Just being able to buy and sell shares quickly with minimal price impact.

Liquidity risk is one big reason why many funds do not purchase shares in very small companies.

If you are the asset manager of a fund with $10 billion in assets, does it make sense to buy shares in a company with a market cap of only $1 billion or less? Say the fund purchases 2% of the company for its portfolio. Now the fund owns stock of $20 million. Or 0.2% of the fund’s assets. Regardless if the company thrives, stagnates, or crashes, it will not have a major impact on fund performance.

Yet if the fund tries to purchase (or later sell) 2% of a small, relatively illiquid, company in the open market, that will move share price significantly. In the wrong direction for the fund.

Note that there tend to be limits on percent ownership in public companies. Often 5% is a threshold. Any more and regulatory complications arise.

Larger Means More Investor Information

Fourth, smaller stocks typically have less publicly available information. I am not referring to corporate filings, such as annual reports or statutory documents. More in respect of investing information.

Many small companies are not actively followed by analysts. Public research or recommendations may be limited. This is compounded by the fact that industry peers are also small firms with relatively little investment information.

The less available information, the less transparency, the greater the investment risk.

Larger May Mean a More Level Field

Fifth, small-cap firms may be closely held by insiders or others connected to the company. While one cannot legally trade on inside information, insiders do have better access to company data and tend to do better than non-insiders.

If you are buying or selling shares in a small company, the counter-party may be someone with more knowledge of the stock than you. This further increases your risk. Whereas if you are buying or selling Apple or Nestle, there are so many shares outstanding that your counter-party is likely someone with similar knowledge as you relating to the company.

When considering investments in small-cap or smaller stocks, be careful.

Key Takeaways

Equities are usually grouped by market capitalization, especially in mutual and exchange trade fund classifications.

Exact splits between segments vary depending on who is classifying the stocks. Ensure you know what ranges make up the segments for the classifier you deal with.

Exact splits are not that important. But understand the broad categories and the characteristics of each. The bigger the company, usually: more information is available for investors; more institutions own the stock; liquidity is better.

The smaller the company, the opposite. Liquidity risk is always a concern. As well, the lack of public information you can obtain and the fact that you are often trading with in-the-know insiders can increase your risk.


More Mean Investment Returns

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.

In my last post we looked at median and arithmetic mean investment returns.

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.