# Lower Risk = Greater Return

While researching index funds, I came across this graph:

I was briefly puzzled. I understand the Modern Portfolio Theory idea that diversification lowers risk. I also see how it can allow higher returns, because riskier investments have higher returns, and with MPT we can choose riskier investments without increasing our risk. But how can it increase return above the return of any individual portfolio component?

Then I did a quick thought experiment. Which has a higher total return, two years of 5% growth, or one year of 10% growth and one year of 0%? The first is 1.05*1.05, or 1.1025. The second is just 1.10. That extra 0.0025 is due to compounding. That second year's 5% acts on 1.05, rather than just 1.00. Some scribbled derivatives later and I decided that for a given total amount of return, optimal growth occurs when the returns are evenly distributed.

So less risk doesn't just let you to choose higher-yielding investments, it also intrisically increases return. Cool.

[Caveat: I think this assumes the ability to costlessly shift money between investments in your portfolio]

## Patri, I'm a futures broker

Patri,

I'm a futures broker at the Chicago Board of Trade. I'd be happy to send you some in depth information on the Modern Portfolio Theory and the use of managed futures. Just shoot me an email & let me know.

## Not a new concept -- it's

Not a new concept -- it's called the "time diversification fallacy." The basic idea is that as the time horizon increases, although average

annualvariation diminishes,totalvariation increases (as you noted, due to the effects of compounding).Stated differently -- which would you rather see if you are 100% invested in stocks: the market decline 50% after your

first yearof investing, or after yourlast year? Yet both are equally likely, ceteris paribus.## Kip - that's interesting, I

Kip - that's interesting, I hadn't read about it before. I found a good article. Its a good observation, but I have some reservations. Its hard for your absolute risk not to be higher just because you have more money. As you say, the stock market can always drop in that last year, when you have the most money invested. Hence why you want to shift your portfolio towards lower-risk investments as you get closer to your target monetary goal.

I wonder if you include an optimal asset allocation, whether risk then decreases with time?