Portfolio risk allocation Math Teaser

[Gazillionaire]

There are 2 types of managed funds. The first is principal guaranteed with a fixed 5% annual return. The second's returns can fluctuate between 20% to -20% annually.
What percentage of funds, say 100k, to allocate to these 2 different investments optimally?
I am interested in a general math formula to combine the 2 types of funds based on maximum downside , maxDD I choose.
For e.g, if I invest 20% in the second and 80% in the first. The worst total fund maxDD is 0.2* -20 +0.8*5=0%

(a) 10% fund B, 90% fund A
Best scenario = 0.1*20+0.9*5=6.5k
Worst = 0.1*(-20)+0.9*5=2.5k
(b) 20% fund B, 80% fund A
Best = 8k
Worst = 0k
(c) 40% fund B, 60% fund A
Best = 11k
Worst = -5k
(d) All in fund A... Fixed return=5k

Which one would you choose and why?

 

[TheDawn]

Well it depends on many factors, my age, my risk tolerance, what you intend to do with my invested money etc. There is no clear-cut answers.

 

[globalarbtrader]

There are 2 types of managed funds. The first is principal guaranteed with a fixed 5% annual return. The second's returns can fluctuate between 20% to -20% annually.

Quite apart from any other information, you haven't told us the expected (average) return of the second fund. Your post implies it's zero. Which means the answer is 100% in the first fund, unless you have a strong preference for risk (politely, you're a gambler)..

GAT

 

[Gazillionaire]

Quite apart from any other information, you haven't told us the expected (average) return of the second fund. Your post implies it's zero. Which means the answer is 100% in the first fund, unless you have a strong preference for risk (politely, you're a gambler)..
GAT

Average return of this new fund is unknown.(past averages is no indicator of future performance). All that is controllable is that the fund will be stopped at -20% or +20%.

 

[globalarbtrader]

Average return of this new fund is unknown.(past averages is no indicator of future performance). All that is controllable is that the fund will be stopped at -20% or +20%.

So there is no information whatseover that would enable me to calculate an expected return for this fund? (track record, historical asset class performance, existence of risk premia, track record of manager at previous fund...)

If there is no information, the expected return can only be zero (maybe negative with management fees). Then why would I invest anything in it?

GAT

 

[MrMuppet]

100% in the first fund. No average performance or drift known for the second one

 

[globalarbtrader]

So there is no information whatseover that would enable me to calculate an expected return for this fund? (track record, historical asset class performance, existence of risk premia, track record of manager at previous fund...)

If there is no information, the expected return can only be zero (maybe negative with management fees). Then why would I invest anything in it?

GAT

Note that the answer would not be zero if we're allowed to rebalance, cost free, between the two assets every year.

Shannons' demon

GAT

 

[MrMuppet]

Note that the answer would not be zero if we're allowed to rebalance, cost free, between the two assets every year.

Shannons' demon

GAT

Interesting idea, really. But that only works if the fund fluctuates between -20% and 25%
If it's either +20% or -20% with a p of 0.5 the expected return is actually negative

 

[Gazillionaire]

So there is no information whatseover that would enable me to calculate an expected return for this fund? (track record, historical asset class performance, existence of risk premia, track record of manager at previous fund...)
If there is no information, the expected return can only be zero (maybe negative with management fees). Then why would I invest anything in it?
GAT

Ok, I came across a fund manager who presented he has 5 years track record of 25% annual return and maxDD=10%(AUM 300mil).
Let this be fund B. How would you allocate now based on fund A and new fund B?

 

[globalarbtrader]

Ok, I came across a fund manager who presented he has 5 years track record of 25% annual return and maxDD=10%(AUM 300mil).
Let this be fund B. How would you allocate now based on fund A and new fund B?

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