Thursday, May 16, 2013

The importance of understanding Total, Average and Annualized Return (CAGR)

As it has been said many times and I am going to say it again ‘we are indeed living in an interesting time’. Stock markets are recording new highs when global economies are deteriorating. Gold, Silver and other precious metals that are suppose to be as safe havens are plunging when central banks are printing more money to reflate stocks and other asset prices. The truth is that the dollar is still declining, the economic recovery that wasn’t, the subprime and housing woes are yet to bottom and if jobs are any indication of economic recovery then high unemployment rates (Portugal 18%, Greece 26% and Spain 27.2%)  in many Western countries suggest that any economic recovery is nowhere in sight.

This is indeed not the time for us to rush and buy more stocks or other assets when accountability and transparency is low. This is the time for us to separate the wheat from the chaff or to separate the good from bad reporting. Take the mutual fund industry as an example even though more than 80% of the funds have problems in keeping up with the index say S&P 500, their marketing department are still dishing out many claims on being number one on this or that category. We as investors especially if you are a value investor it is important for us to differentiate what is reported especially earnings or returns really justifies. In the following we present to you the three methods of calculating returns of an individual stock or Portfolio.

Total Return

This is the first method in determining not only how well your individual stock but also the entire portfolio performed over a period of time.  The formula is as follows.

Total Return = (Current Value – Original Value) / Original Value

Say for example if you bought a stock at $20 and now trading at $30 then the percentage your stock gained can be calculated pretty straight forward.

($30 - $20) / $20 = 0.50   or 50% return

Again, it can also be used to calculate the performance of an entire portfolio. Say if your portfolio values at $1200 on January 1st 2012 then on December 31st 2012, your portfolio is worth $1600 then we apply the same formula again.

($1600 - $1200) / $1200 = 0.333   or 33.3%

Average Return

Average Return is obtain by adding several values say five values together and then divided by five.  To understand this we present you the following example of five annual returns of an individual stock.

To calculate the average return we add up the returns and divide by 5. Hence,
(25-7+14+75-10) / 5 = 19.4%

Annualized Return or CAGR

The problem with both the above approach is that due to their individual reporting, to calculate an annual compounding rate of return from them is not possible. The Total and Average Return approach does not take time into consideration as only values are used and hence does not take compounding into consideration. As a result they tend to produce an over estimation of return on an investment. The annualized return or compound annual growth rate (CAGR) approach includes time (normally in years) and thus enables us to calculate the annualized return of an investment whether it is a short or long term.  

The following is the formula for calculating the CAGR for an investment.

Annualized Return (CAGR) = (Current Value / Original Value) ᴧ (1 / years) – 1

Where, the symbol ᴧ denotes an exponent.

To illustrate we shall use the following short term example,

Starting Capital or Value - $15,000
Duration – 5 months or 0.4167 (5/12)
Current Value = $16,800

(16800/15000) ᴧ (1/0.4167) – 1   which will produce,

1.12 ᴧ 2.4 -1 = 0.3125 or 31.25% annualized return.

Why Average Return overestimate growth?

To answer the above question we present to you again the example which displays the annual growth rate of stocks.

To calculate the Average Return we add up the returns and divide by 5. Hence,
Average Return = (25-7+14+75-10) / 5 = 19.4%

The problem with average return approach is that it did not take into consideration the compound annual growth rate of returns for the different years which include both positive and negative returns. To have a better picture we shall calculate the CAGR of the above investment with the following assumptions.

Starting Capital or Value - $10,000
Duration – 5 years
Current Value = ?

The following chart shows the current value from an investment of $10000 with the above returns.

So, in year 5 our portfolio is worth $20873. To calculate the CAGR we just substitute the figures into the following formula.

Annualized Return (CAGR) = (Current Value / Original Value) ᴧ (1 / years) – 1

(20873/10000) ᴧ (1/5) – 1 = 0.1586 or 15.86%

Thus, you can see that the annualized return of your portfolio is actually lower than your average return of your portfolio.

So what?

So what is the fuss if you know the differences between those two? Well it does help you in evaluating the figures reported in the media or advertisements by companies or mutual funds about their past performance. Take for example the following advertisement.

Our Portfolio is up 1000%
                                     (over the past 25 years)

By the first look it looks very promising and impressive but when you look at the fine print it is over a period of 25 years. Let see what happens when we applied it to the CAGR formula. Again we use the following assumptions.

Starting Capital or Value - $10,000
Duration – 25 years
Current Value = $110,000 (1000 %  appreciation)

($110000 / $10000)  ᴧ (1/25) – 1 = 0.1007 or 10.07%  per year for 25 years


Our Fund averages 19.4% return past 5 years

So it is not so impressive after all, right? One thing for sure is that we will not be their next ad-sucker victim.

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