Risk "drag" in investing, poker

[DesertCat]

Volatility is not risk, hence CAPM is bunk.

I will point out if you are continuing to add to your investments (i.e. dollar cost averaging or reinvesting dividends) you want as much volatility as possible as it will lead to higher returns. For example, assume you have an investment that doubles from $10 to $20. One progression is $10, $11, $12, etc over eight years ending in $18. Another progression is $10,$8,$12,$10,$14,$12,$16,$14,$18 also ending in $18. If you reinvest fixed amounts every year, the second progression offers you a substantially better return, even though both begin and end at the same endpoints.

[edtost]

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Volatility is not risk, hence CAPM is bunk.

I will point out if you are continuing to add to your investments (i.e. dollar cost averaging or reinvesting dividends) you want as much volatility as possible as it will lead to higher returns. For example, assume you have an investment that doubles from $10 to $20. One progression is $10, $11, $12, etc over eight years ending in $18. Another progression is $10,$8,$12,$10,$14,$12,$16,$14,$18 also ending in $18. If you reinvest fixed amounts every year, the second progression offers you a substantially better return, even though both begin and end at the same endpoints.

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note that the same logic applies to rebalancing a portfolio to fixed %ages in each asset even if you do not put any more money in.

[Scorpion Man]

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are you really trying to say that the CAPM isn't up for debate, as it applies to real financial markets (not as a theoretical construct)?

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CAPM as a whole, and in terms of its robustness, is definitely up for debate. Whether risk and return have any relationship at all I don't really think of as up for debate.

And, regardless, it does not really matter...because I don't need CAPM to be right to make Mr. Now's original post incorrect. It's just as easy to come up with scenarios where higher vol returns beat lower vol returns as vice versa.

In addition...riskier assets have had empirically higher returns over history. If you don't think so, I dont know why you would ever buy a stock again. Put it all in in 30 day treasury notes. I am sure it will outperform my stock portfolio.

[edtost]

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I would just like to add, whatever your opinion of SM, it cannot be debated that he is a great addition to this forum. Great thread so far, enjoying reading even if I'm too dumb to contribute further [img]/images/graemlins/smile.gif[/img]

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i think SM is both a smart guy and a good thing for the forum, but that he is completely missing the point of the OP in this particular case.

[Scorpion Man]

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I would just like to add, whatever your opinion of SM, it cannot be debated that he is a great addition to this forum. Great thread so far, enjoying reading even if I'm too dumb to contribute further [img]/images/graemlins/smile.gif[/img]

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i think SM is both a smart guy and a good thing for the forum, but that he is completely missing the point of the OP in this particular case.

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Thanks for kind words, guys. I capitulate. As narrowly stated, OP is correct. I was reacting to what felt like the implied message of the post...that volatility/risk is bad and to be avoided.

[danny31415]

Well, I think it depends on what you means by "average annual return". If by average you mean just take the average (arithmetic mean the average everone learned when they were in elementary school) of each years returns, then you're right.

But the arithmetic mean does not make much sense when talking about annual returns. For instance If I make 200% every year for 5 years, then I lose everything(-100% gain) the 6th year, I get an average return of (200 * 5 - 100) / 6, or 150% average annual return, but an overall return of -100%.

If you use the geometric mean (same as compound annual return in the article) though things change. I am pretty sure that two investments with the same (geometric) average return will always have the same overall return.

It seems like the linked article uses the arithmetic mean to quote average annual return, but I find it hard to beleive that people actually quote that number in practice. If I go to vanguards site and see the 5-year performance of one of their funds which one do they show me? It seems like it is a deceiving to show the arithmetic average annual return, I would think the SEC have regulations about how you quote your average annual returns? If not then I have a new buisness selling securities that have a high average return, in fact I'll lay it out here. At the end of every year I flip a coin and if it is heads then the security triples in value (200% return) if tails then it quarters in value (-75% return). The average return will be 62.5% a year but I will take ~16% of peoples money every year, I'll be rich.

[maxtower]

Sounds like you guys are arguing the same thing.
I'm sure everyone here expects more risk can lead to better returns.
Average annual return and compunded return are not the same thing, thats why all these examples make the more volatile returns look worse. If your first year out of the gates is a down year, you'll never recover with the same "average annual return". This shouldn't make your scared of increased risk however or volatility. As pointed out above, increased risk can mean larger returns, and DesertCat points out that increased volatility is better for the dollar cost averaging investor, which is how most of us invest anyway since we are adding money every year.
Max

[NajdorfDefense]

compound/geometric return is the correct metric, not average annual.

Increased risk <> increased return, ceteris paribus, otherwise you could spend the rest of your $$$ on lotto tix tonite and go home happy.

Vol <> risk.

[Scorpion Man]

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compound/geometric return is the correct metric, not average annual.


Increased risk <> increased return, ceteris paribus, otherwise you could spend the rest of your $$$ on lotto tix tonite and go home happy.

Vol <> risk.

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I think I have seen you write this elsewhere. Can you elaborate, please? I just got off the phone with some hedge fund PhDs...my understanding is that volatility = one standard deviation of returns (assuming log normal distribution).

Chapter 3 of Grinold and Kahn -- Active Portfolio Management...its the standard textbook ... "risk is the standard deviation of return"

I guess that risk does not have a single definition.
Volatility is a FORM of risk.
Barra (popular wall street quant software) breaks risk into 68 different factors (industry, country, cap, style, etc).

In a general sense, risk is anything that can happen that you cannot predict.

Volatility is not the ONLY kind of risk...there is a Sortino ratio that adjusts for upside moves versus downside moves...i.e. if you have a fund that is always up but how much it is up changes a lot...this is a "risky". That goes against how most of us would think about "risk". Sortino adjusts for this.

So, most of us are worried about "downward volatility". That said, at first blush volatility of return is a good proxy for risk.

My buddies are saying there is no standard mathematical definition of "risk". Many people substitute volatility for this in practice.

My friend, who runs $1b hedge fund and owns it 100%, says in his opinion most folks who run portfolios and quant funds (he has quant as well as long/short) would say risk = volatility.

That is also how we looked at it in my shop...but we were not very quant oriented.

Dan