Re: portfolio management

From: John Conover <>
Subject: Re: portfolio management
Date: Sat, 19 Sep 1998 22:05:33 -0700

John Conover writes:
> But there is a problem; the portfolio will not be volatile enough for
> maximum growth. Why? Because investors in the US markets are risk
> adverse, (we can measure exactly how risk adverse because when
> optimal, rms = 2P - 1, which results in rms = sqrt (avg), and metrics
> on the stock exchanges indicates that rms is too small, ie., investors
> are reducing volatility at the expense of long term growth.) There is
> a solution to this problem, and that is to reduce H to less than
> unity, ie., manage the portfolio by inter-day trading, (this is what
> the programmed traders do.) This is not a viable alternative for most
> investors, so most investors will have to exercise the remaining
> alternative, which is to minimize long term risk-and we know how to do
> that-just make P unity, ie., a probability of 100% on any given day of
> an up movement in the portfolio's value. And, that occurs where:

Can the portfolio growth be made optimal? Yes, for example, by buying
stocks on margin, (I'll show that margins are not a practical strategy
when building a stock portfolio,) using the exact same methods we have
been using all along-and it too can be optimized-ie., the portfolio
growth can be maximized, while at the same time minimizing risk
exposure to the margin calls. The tsstock program, (which is not part
of the tsinvest suite-it is part of the suite in,) can be used to do it.
The trick is to buy enough, (but not more or less,) of the initial
investment in a group of stocks that make up a portfolio on
margin. How much on margin? It turns out to be:

    F = ----

where avg and rms are the average and root mean square of the marginal
increments in the portfolio's value without using margins, and F is
the fraction of the portfolio that would be purchased initially on
margin. Using 10 stocks from the NYSE in the portfolio, and
re-balancing the portfolio annually, the characteristics of the
portfolio without any margin purchases would be:

    avg = 0.000270
    rms = 0.008780

giving a liklihood of an up movement on any day, P, of:

        avg        0.000270
        --- + 1    -------- + 1
        rms        0.008780
    P = -------- = ------------ = 0.515375854
           2            2

which would grow at, G:

                      0.515375854                 (1 - 0.515375854)
    G = (1 + 0.008780)            * (1 - 0.008780)

      = 1.000231488

per day, or for 253 trading days in a calendar year:

    G = 1.000231488    = 1.06030828

However, if, (by some means,) the stock investment could be made

    F = --------- = 3.502472486

times larger, my fraction of the investment would grow, optimally. So,
for every dollar I invest in such a portfolio, I get on margin, (or by
borrowing,) 3.502472486 dollars to invest additionally. Then,
characteristics of my portion of the portfolio with margin purchases
would be:

    avg = 0.000942
    rms = 0.030698

giving a liklihood of an up movement on any day, P, of:

        avg        0.000942
        --- + 1    -------- + 1
        rms        0.030698
    P = -------- = ------------ = 0.515343019
           2            2

which would grow at, G:

                      0.515343019                 (1 - 0.515343019)
    G = (1 + 0.030698)            * (1 - 0.030698)

      = 1.000471001

per day, or for 253 trading days in a calendar year:

    G = 1.000471001    = 1.126522269

or, a little more than doubling my returns per year on my fraction of
the investment.

What are the risks? The risks are that I could loose my investment,
and some of the margin. But what is the risk of that happening? The
strategy is the most vulnerable in the first five years-after that,
the portfolio has increased in value sufficiently to be able to
tolerate a market drop of 30%, (which is about the value I would have
in my fraction of the portfolio. At that point, I may loose my
investment, but I would be able to sell the remaining portion and, at
least, respond to a margin call.) So, we are really asking what are
the chances that the market will drop more than 30% in 5 years. The
standard deviation of the portfolio, in 5 calendar years of 253
trading days would be the rms * sqrt (5 * 253) = 0.030698 *
35.56683849 = 1.091830808. What that means is that I would have about
a one third standard deviation chance of NOT going bust, or about a
38.2088% chance of NOT going bust, which means a 61.7912% chance of
going bust.

Not a good deal. Bear in mind that if you use margins, this is the
best risk/gain scenario that is possible. Using less margin, or more,
will increase the risk of going bust, and, at the same time, lower the
gain you would achieve buy using margins.



John Conover,,

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