Portfolio risk allocation Math Teaser

Gazillionaire · Sep 27, 2022

globalarbtrader said:
It depends on my degree of confidence in those figures, the chance of them continuing in the future, the expected distribution of returns, my risk preferences, and a whole bunch of other factors.

You are asking what you think is a simple question, but it doesn't have a simple answer. We need to make a lot of assumptions to get a tractable answer.

Let's assume I am risk neutral, so I want to maximise expected returns. Let's also assume I am 100% confident that the track record will continue. Let's finally assume that the profile of the fund is that there is a 50/50 chance that the return will be -10% and a 50% chance it will be +35%. That gives an arithmetic average of 25% a year (geometric return will be a bit lower).

Then to maximise expected return I would put 100% of my money in the risky fund B (expected return, 25% vs 5%).

Now you want to impose a maximum drawdown constraint. The maximum d/d and expected return would be:

100% in A: zero d/d, expected return 5%
50% in A: -5% d/d, expected return 15%
100% in B: -10% d/d, expected return 25%

Depending on your max d/d constraint you'd pick from one of these options, or an interpolated version. That's a pretty trivial exercise of course, but then I'm not sure what you hoped to get out of asking this question?
GAT
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"The chance it will continue into the future"
That's funny.

FreeGoldRush · Sep 27, 2022

You need to decide on a probability distribution for the second fund. If you assume Gaussian, as we usually do since we have no idea, then don't put any money into the second fund because you have obviously calculated an average return of 0% annually.

earth_imperator · Sep 27, 2022

I just wondered why there is no page yet about "Shannon's daemon" in wikipedia.
Also good about the same topic is this referenced link and this in the above text.

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Portfolio risk allocation Math Teaser

Which allocation?

A

B

C

D

Gazillionaire

FreeGoldRush

earth_imperator