Does Volatility Hurt Real Returns?

[rokid]

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Does volatility hurt returns? Yes!

Most of us calculate average return to determine how well our investments are doing. In addition, we use the arithmetic average of a series of annual returns to determine how well we’ve done over a number of years.

In fact, we should also calculate the annualized return. The annualized return takes volatility into account.Annualized return is our real return and is always less than the annual return. Annualized return is what we can actually spend.

For example:

Years 2000-2004
Average Standard Annualized Compound
Annual ReturnDeviation Return Return

Tom 4.62 22.582.77 1.15
S&P 500 -.75 20.26 -2.34 .89
*60/40 Stocks/bonds 3.34 12.262.78 1.15
*20% each fund 3.37 13.662.68 1.14
100% G Fund 5.044 0.935.041 1.28

* Passive allocation without rebalancing

Note for eachportfolio example, the annualized return is less than the average annual return. In addition, although Tom’s average annual return is 1.28 percent higher than the 60/40 allocation, his annualized return is a hair lower (.01 percent) because of his portfolio’s higher level of volatility.The S&P 500's annualized return (-2.34) is also significantly worse than its average annual return (-.75) because of its high level of volatility. In contrast, the G Fund's annual and annualized returns are almost identical because of the G Fund's low level of volatility.

Finally, the “Compound Return” represents the 2004 nominal value of a dollar invested in 2000 for each of the portfolios. Tom's and the 60/40 allocation's compound returnsare identical at 1.15, closely followedby the 20% each fund1.14 compound return.

Conclusion: Return and volatility count - not just return. The higher the volatility the greater the gap between annual return (what everyone reports) and annualized return (the real return thateveryone spends).

 

[Guest]

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Rokid...

 

[tsptalk]

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rokid wrote:

Conclusion: Return and volatility count - not just return. The higher the volatility the greater the gap between annual return (what everyone reports) and annualized return (the real return thateveryone spends).

Excellent explanation rokid. Thanks!

 

[Pete1]

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Thanks for posting this, Rokid. A wonderful piece of analysis. I have saved the worksheet for future reference.

 

[rokid]

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Thanks guys and WW. I glad you found it interesting/useful.

 

[tennisguy]

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If you don't mind can you explain to me how you get those numbers. And why are the annualized returns are your real returns instead of your annual return.
Thanks
Tennisguy

 

[rokid]

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tennisguy wrote:

If you don't mind can you explain to me how you get those numbers. And why are the annualized returns are your real returns instead of your annual return.
Thanks
Tennisguy

Tennisguy,

What I tried to say is that your annualized return (geometric mean) is your real average return over a number of years. Your average annual return. i.e. arithmetic mean of your annual returns, is not.

For example, if you calculate the compound return using Tom's actual annual returns, you get a factor of 1.15. In other words, if Tom invested a dollar in 2000, he had $1.15by the end of 2004. In contrast, someone who went 100% C Fund through the period2000-2004, had $.89by the end of 2004. Clearly Tom did better.

However, if you assume Tom's average return over the period 2000-2004 was 4.62% (arithmetic mean), you would be incorrect. If your use 4.62% to calculate the compound return over the period 2000-2004, you get 1.25, which is incorrect. If, on the other hand, you use Tom's annualized return, 2.77%, you get the correct compound return.

The only interesting point about all of this is that volatility counts. If you have zero volatility, your annual average return =s your annualized return. However, any volatility causes the two to diverge. The greater the volatility, the greater the divergence between your average annual return and your annualized return. Finally, as previously stated, the annualized return is your real average return and is always less than or equal (no volatility) to your average annual return. Therefore, one of an investor's strategies is toreduce returnvolatility.

Examine the cells in the attached spreadsheet for more info. I updated it to show the difference in compound returns (correct vs incorrect).

Finally,I used Excel’s geomean function to calculate the annualized return.

I hope that helps.:^

 

[Pete1]

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Here is another rather simplistic illustration. Two individuals have average annual returns of 10% per year. Investor A's returns are: year 1+30, year 2-10, year 3+30, year 4 -10. Investor B's returns are: +10, +10, +10, +10. Both have average annual returns of +10 but who has more money? Answer - Invesor B.

Assume both start year one with $100000. Results after 4years:

Investor A: end of year one = $100000 x 1.3 = $130000,end of year two = $100000 x .9 = $117000, end ofyear 3 = $117000 x 1.3 = $152100, end of year four = $152100 x .9 = $136890.



Investor B: end of year one = $100000 x 1.1 = $110000, end of year two = $110000 x 1.1 = $121000, end of year three = 121000 x 1.1 = $133100, end of year four = $146410.

Both have average returns of 10% but the less volatile portfolio puts more food on the table.

 

[Mike]

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That is probably why they tell even young investors to have *something* in bonds to balance out the aggressive holdings. Not only does that reduce overall risk, but it also knocks down the volatility a bit.

 

[tennisguy]

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Thanks guys , I understand a whole lot more now.
Tennisguy

 

[charmedboi82]

Of course, you can't average an average. It's extremely misleading. Thankfully, I learned this in seventh grade from a crazy (seriously) teacher.

 

[rokid]

Charmedboi82,

I'm not sure what your point is. I don't see where anyone on this thread said anything about averaging an average. However, you can take the average of a set of averages. For example, the average of 30 daily temperatures for the month can yield an annual monthly temperature.

Anyway, the discussion was about average returns, which don't take volatility into account, and annualized/geometric returns which do. Annualized returns are actually the average compound return over a period. Annualized returns are always lower than average returns. In addition, the greater the volatility, the greater the difference between the average return and the annualized return.

 

[charmedboi82]

Charmedboi82,

I'm not sure what your point is. I don't see where anyone on this thread said anything about averaging an average. However, you can take the average of a set of averages. For example, the average of 30 daily temperatures for the month can yield an annual monthly temperature.

Anyway, the discussion was about average returns, which don't take volatility into account, and annualized/geometric returns which do. Annualized returns are actually the average compound return over a period. Annualized returns are always lower than average returns. In addition, the greater the volatility, the greater the difference between the average return and the annualized return.

Call it what you will. In my mind, the difference that you referred to is adequately expressed by what I said. You just seem to refer to it by different terminology.

It's why it's very misleading when people quote what the market has done for the past decades. Just because it was up an average of X% doesn't mean that you would have received a return value as though it had gone up that average percent every year.

So, I really do believe it is the same thing. I just choose to express myself differently.

 

[rokid]

It's why it's very misleading when people quote what the market has done for the past decades. Just because it was up an average of X% doesn't mean that you would have received a return value as though it had gone up that average percent every year.

So, I really do believe it is the same thing. I just choose to express myself differently.

In that case, I agree with you 100%.