SERVING THE QUANTITATIVE FINANCE COMMUNITY

alpher
Topic Author
Posts: 90
Joined: September 1st, 2012, 4:20 pm

Can some of you genuises explain why investing LESS than half of your capital will always result in multiple times ROI?

Apparently if you "modify" the Kelly criterion (log of your capital) it turns out that if you invest less than 50% of your capital in ANY investment, as bad as it is, results in increase of wealth over time, assuming the worst that could happen is loosing everything while the best is 'infinite upwards potential' or at least increase over the years.

In other words, assume investor John who in 1990 or so invests less than 50% of his money in random pool of stocks or just MSFT (random investment but he may believe they're winners for some bizarre unfound reason!). John knows the worst that can happen is loose his money as stocks are 'risky' but he knows after decades the value may go up, he will be rich today for as long as he invests always <50% of his loses/gains.

I know what you're thinking but if John invests more than 50%, say 80% of his money without understanding the market he or his successors will ultimately end up with 0\$, loosing everything...so being 'brave' and 'big player' here isn't justified unless you have VERY serious reason to believe the market will go up...obviously you can invest less but you'll be leaving 'money on the table'.

I am tired now to give some mathematical representation of the above short essay .

ppauper
Posts: 70239
Joined: November 15th, 2001, 1:29 pm

Re: Can some of you genuises explain why investing LESS than half of your capital will always result in multiple times R

the geniuses (genii?) are busy so I'll pitch in
Kelly criterion
Apparently if you "modify" the Kelly criterion
and of course you haven't told us what the "modification" is, which makes answering your specific query a tad difficult as we don't know what it is
it turns out that if you invest less than 50% of your capital in ANY investment, as bad as it is, results in increase of wealth over time, assuming the worst that could happen is loosing everything while the best is 'infinite upwards potential' or at least increase over the years.
in ANY investment, as bad as it is
is inaccurate for the standard Kelly criteria, as wiki tells us
If the edge is negative (b < q / p) the formula gives a negative result, indicating that the gambler should take the other side of the bet.

Alan
Posts: 9650
Joined: December 19th, 2001, 4:01 am
Location: California
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Re: Can some of you genuises explain why investing LESS than half of your capital will always result in multiple times R

Even with a positive edge, it's easy to cook up examples where a repeated, say, 45% allocation to a risky bet will result in essentially losing everything over time.

For example, take a weekly allocation to a long call option (expiring in 1 week)  with say, a 50% chance of +150% return and a 50% chance of -100% return (call expires worthless).  These are the returns on the 45% of your money allocated to the calls. The return on the remainder 55% of the portfolio (say cash) is zero. Although the expected portfolio return is quite positive, within a couple years you'll almost certainly have less than 1% of your initial wealth.

So, OP's statements about allocating less than 50% to "any" investment are generally wrong. If you restrict the universe to, say, low-cost cap-weighted index funds of US stocks -- well, different story, of course, and you'll probably do ok over time with my example 45% weight.

ppauper
Posts: 70239
Joined: November 15th, 2001, 1:29 pm

Re: Can some of you genuises explain why investing LESS than half of your capital will always result in multiple times R

Alan's one of the geniuses here, so the OP has got at least one answer.

I'm still not sure what the modification to the Kelly criterion is

For an example like the one Alan posted, the Kelly criterion tells you to invest a fraction

$f^{*}=\frac {\text{expected net winnings}}{\text{net winnings if you win}}$

which works out to 1/6 or 16.66667% for Alan's example, considerably less than the half mentioned in the thread title