What percentage of funds to allocate to different investments optimally with rebalancing?

There are 2 types of managed funds. The first is principal guaranteed with a fixed 5% annual return. The second's returns is between 20% to -20% annually. Is there a way to roughly calculate what percentage of funds to allocate to each of them based on maximum drawdown I choose,say 10%, of total amount I have?

Is there an efficient frontier point formula to find the best balanced combination of some fixed return + some randomness given user defined maxDD and best scenario return?

Let me simplify the choices based on \$100k principal:

(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
``````

What about using volatility swings to create a bias... Can you rebalance them every year or whenever fund B reaches +20% .i.e divide just fund B's profit only(or loss) by 2 and reinvest in both equally such that in the long run the equity curve is bias upwards? https://rsharat.substack.com/p/shannons-demon-parrandos-paradox

• Is this a real world example or did you make up the numbers? If you chose the numbers yourself, you may want to pick different returns for the 2nd fund (or maybe define that -20% is x% less likely than +20%), as random returns of -20% to 20% result in a negative average return. Maybe try -10% to 20% or something to (maybe) get sensible answers to a situation you are actually interested in. Commented Sep 26, 2022 at 9:29
• The Kelly criterion? Commented Sep 26, 2022 at 18:09
• There's no particular optimization because the collar of Fund B has some underlying position and then some fundamental viewpoint, but not a probability, of likelihood or risk. But logistically, set-up the equations based on an acceptable worst case and then calculate the percentages of the two investments. Finally, note the best case result. Commented Sep 27, 2022 at 7:59
• Assuming (!) your fund B has its return uniformly distributed from -20 to +20, a simple look at your examples should show the obvious pattern (hint: the more fund B you add, the worse the midpoint return becomes...) Commented Sep 28, 2022 at 9:17
• Yes, the midpoint is indeed<5. Thanks. Does this mean that if any fund has a record of 25% return but -10% maxDD, with midpoint 7.5, one should go all in it instead of having any % in fund A at all? Commented Sep 28, 2022 at 10:43

This is a completely meaningless exercise as is; to calculate anything at all meaningful you need to estimate the average return of the second fund and its variability. Good investments with high variability will have higher average return than investments with guaranteed return. In particular, if the second fund is assumed to have returns equally distributed between 20% and -20% (a behavior which does not occur in any real investment,) then it would be a horrendously bad investment.

• Real world beta changes all the time. Commented Sep 27, 2022 at 6:49
• If you know the word beta, then you should understand perfectly well why your question is unanswerable. Commented Sep 27, 2022 at 20:46

Be wary of guarantees.

Assuming it's truly guaranteed, you can simply calculate the returns and invest in whichever account gives you more. This sounds like a theoretical exercise. It's unlikely that your results will translate to the real world.

In this case, the 5% is going to win since without more info, I'd take the average of the 2nd one, which is 0%. You'll need historical returns for the 2nd one.

The reason people invest in multiple accounts is to not be ruined if one of them is run by a Burnie Madoff. Google "dollar cost averaging", which I think is what you want.

• 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 maxDD is 0.2* -20 +0.8*5=0% Commented Sep 26, 2022 at 15:22
• The math is really simple. Investment * 0.05. Commented Sep 26, 2022 at 16:39
• because fixed 5% = 0.05. The other investment averages to 0% Commented Sep 26, 2022 at 18:28

Oh, the investor has one fund guaranteed at 5% gain and a second fund guaranteed at between 20% and -20%. Then the investor wants to speculate on making more than 5% in the second fund. However, the investor wants to calculate the amount of investment in each fund so as to limit the possible overall loss.

Note that "x" represents Fund A and "y" represents Fund B:

For a possible overall loss of 10%, then .05x - .20y = -10 and 1x + 1y = 100 for an x,y solution set of {40 , 60}. Or for a possible 0% overall loss, then .05x - .20y = 0 and 1x + 1y = 100 for an x,y solution set of {80 , 20}.

In the first calculated case, the maximum possible gain is 14%. In the second calculated case, the maximum possible gain is 8%.

Also, consider a positive return for a worst case as .05x - .20y = 2.5 and 1x + 1y = 100 for an x,y solution set of {90 , 10}. Then the best case in this instance is a 6.5% return.