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Effect of high variance on the return calculated by MC

Submitted by TagVW@comcast.net on 16 June 2010 - 8:51pm

I have been puzzled by higher simulated returns in the MC than I would have expected based on manual calculations. After Larry suggested a test using a single asset for another reason, I used that idea to test the effect of variance.

The table below shows that the mean return increased and the spread between the mean and the median increased with higher variance. Does this explain why my portfolio, which includes several high variance assets, produces a higher return than I expected?

There were articles on the web about this but they went quickly beyond the reach of my sparse training in statistics. The first column shows the variance of the user defined asset. The others are the portfolio characteristics produced by the Monte Carlo. Every asset was defined with a mean real return of 15% and Beta of 1.0. The beta for the results was also 1.0.

............ Variance----||Mean. Median Var..
Portfolio 2 0.0000%--||15.0% --15.0% 0.000
Portfolio 3 25.000%--||15.1% --14.5% 0.250
Portfolio 4 50.000%--||15.2% --14.1% 0.499
Portfolio 5 100.00%--||15.5% --13.2% 1.010
Portfolio 6 200.00%--||16.0% --11.6% 1.989
Portfolio 7 300.00%--||16.9% --10.0% 3.004
Portfolio 8 400.00%--||17.7% ---8.7% 4.015
Portfolio 9 500.00%--||18.1% ---7.2% 4.992

Thank you for any light that you can shed on this for me.

‹ Role of inflation rate in MC Long term high inflation and our suggested consumption in real dollars goes down a relatively small amount? How can that be? ›
Submitted by Dick Munroe on 17 June 2010 - 5:11am.
1

At least in part, what you're seeing is the effect of the probability distribution. The math uses what's called a log-normal distribution to avoid the problem of dealing with discontinuities associated with taking the log of 0 (an undefined value in mathematics). This curve stops at 0 and has a long "tail" (to the right looking at a graph) where the low probability, higher returns happen. The higher the variance, the more weight the tail has, thus the increase in the mean and the differences between the mean and median. I may have gotten this wrong and Larry will chime in, but I think that's what is happening here.

Best,

Dick Munroe

Submitted by TagVW@comcast.net on 17 June 2010 - 6:16am.
2

Thank you for the clarification. I was able to picture the distributions but not the effect on the MC. So the return goes up because the MC is taking random samplings from the curve. If that curve has more locations with higher returns, it will produce a higher return overall?

Tag

Submitted by Dick Munroe on 17 June 2010 - 12:23pm.
3

As long as the "tail" portion of the distribution gets "heavier" then I believe the answer is yes. In the interests of full disclosure, I am most definitely NOT an economist or statistician (although I've picked up bunches of both from Larry) so take anything I say with a grain of salt until Larry chimes in.

Best,

Dick Munroe

p.s. http://en.wikipedia.org/wiki/Log_normal has a pretty good explication of what log normal means and some nice pictures that may make things easier to visualize.

Submitted by TagVW@comcast.net on 17 June 2010 - 12:49pm.
4

Thank you, Dick. I appreciate the pictures in wikipedia; the words will take longer to penetrate.

Regards, Tag

Submitted by Dick Munroe on 20 June 2010 - 4:26pm.
5

We're looking at the issue. No resolution yet because everything looks like it's right.

Best,

Dick Munroe

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