# Category based ranking makes sense

Here is an example,

5 cents stock option could be easily valued 5 dollar tomorrow or it could be zero. So the variation could be -100 to 10,000%

Based on Nasdaq 5-10 years history odds of nasdaq % change tomorrow is -10 to 10 % If tomorrow is most volatile day in the history then it will hit -10% or +10%

We can’t rank them based on % return only, how about different categories for different type of systems.

By the way, 0.05 option will have bid:0.05 and ask:0.1 and I don’t think it’s difficult to buy that option at 0.05 and sell it at 0.1 in few hours

If I do that tomorrow is my system really no.1?

Give it a try and see what happens.

In real life, the price of that .05 cent option would go up the moment you buy the first quantity of 10 that are being offered by the market makers.

The market makers aren’t dumb.

MK

There are numerous investors whose main objective is to maximize the expected geometric average rate of return of their portfolio. Examples of investors with such preferences are proprietary traders and hedge-fund managers. Hedge-funds as you may know approached 1 trillion dollars in assets at the end of 2004.

I would think that one would require an unusually large quantity of options to bid the price up from 5 cents to \$5. Even with a large number of options, a mean-square-optimal portfolio need not come close in certainty equivalence to the optimal dynamic investment policy. Studies have shown that as the number of options increases, the investor’s welfare increases, so that for say 5 options (n = 5), the certainty equivalent (CE) of the optimal buy-and-hold strategy is around 34.9% of the CE for the optimal dynamic stock/bond policy. Although this is a considerable improvement over the case where thare are no options (n = 0), it is still quite far below the optimal dynamic strategy’s CE. As the number of options increases beyond 5, this approximation will improve eventually, but the optimization process becomes considerably more challenging for larger n. For example, the n= 15 cases involves (45 strikes 15 options) factorial = 344 867 425 584 sub problems, and even if each subproblem requires 0.01 seconds to solve, the overall optimization problem would take approximately 109.4 years to complete. When options are allowed in the buy-and-hold portfolios, additional risk-reduction possibilities become feasible and the optimization algorithm takes advantage of such opportunities. Call options are generally more sisky than the underlying stock on which they are based. See for example, Cox and Rubinstein (1985) Options Markets (Englewood Cliffs, NJ: Prentice Hall). The stock returns are more predictable, hence there is greater value to be gained from investing in stocks for each level of risk aversion compared to options. Alternatively, the predictability in stock returns make stocks less risky, ceteris paribus, hence even a risk-averse investor will hold a larger fraction of his wealth in stocks in this case. However, unlike the geometric Brownian motion case, the optimal buy-and-hold portfolios do contain short positions in some options, even for lower levels of risk aversion. For higher levels of risk aversion, the situation is reversed: the optimal buy-and-hold portfolios are net negative in options, but they do contain long positions in certain options.

The CE of the optimal buy-and hold portfolio do not increase monotonically as the number of options increases, since we are optimizing mean-squared error, not expected utility. However, for higher levels of risk aversion, the CE do tend to increase with the number of options in the portfolio (and are guaranteed to converge to the upper bound as n increases without bound). As risk aversion increases, the optimal buy-and-hold portfolios behave in a manner where the options are used to hedge long positions in the stock. For very high risk-aversion levels, all options positions are negative (put options - short on a call option).

The inclusion of a few well-chosen short-maturity options from time to time in an otherwise passive buy-and-hold portfolio might be a very cost-effective alternative to the optimal dynamic asset allocation policy.

There are numerous computational challenges associated with the optimization procedure that arise in the practical implementation of the optimal buy-and-hold strategy that involve options. Specifically, there are limits to the number of subproblems that can be handled in a reasonable amount of time, which imposes limits on the number of possible strikes that can be considered, as well as the number of options (n) in the buy-and-hold portfolio. We need not limit ourselves to just 45 strikes for a particular (n=1) option, when solving for the optimal buy-and-hold portfolio.

This only underscores the complexity of an investor’s ideal risk exposures. It would be nice to be able to gain insight into the implicit bets that a particular dynamic asset-allocation strategy contains, and develop a standard lexicon for comparing those bets across investment policies. Optimal dynamic asset-allocation policy is generally unattainable due to transaction costs and other market frictions, but can be approximated with just a few options given that only a few trades are required to establish the portfolio and there are few costs to bear thereafter.

An even more compelling motivation for the optimal buy-and-hold portfolio is the presence of taxes. For taxable investors, the CE is reduced by the present value of the sequence of capital gains taxes that are generated by an optimal dynamic asset-allocation strategy. In contrast, all of the capital gains tazes are dererred untial a future point in time in a buy-and-hold portfolio. Therefore, the economic value of predictability is likely to be even lower for taxable investors, and the optimal buy-and-hold portfolio that much more attractive. The main challenge is tractability and computational complexity.

Deriving optimal buy-and-hold strategies to approximate other than dollar-cost averaging strategies or other popular dynamic investment strategies - stragtegies that need not be based on expected utility maximization might be of considerabely lesser interest. We have to examine the payoff structure of the portfolio and its sensitivities to various market factors and economic shocks.

rgds, Pal

Midas Value

If I do that tomorrow is my system really no.1?

Sure. But that doesn’t mean you will have the most subscribers.

Subscribers look at risk/reward ratios and just because you can make a few lucky (but very risky) guesses they won’t sign up for your luck. There are already enough information on systems, they can choose according to their tastes. There is no need to make Matt’s job more difficult than it is.

All I want to say is different type of systems has different risk/reward ratio range. And i don’t have subscribers survey report to guess what subscribers really want. I know for sure that they are not looking for lucky systems.

as a theory

what you say makes sense , however the predicablity of

returns on stocks does not make them a safe bet . less risky

to an option because of no time decay , yet still no predicable return that has any real sound basis , historic basis yet . if the stock mkt hence stocks did have a predictable return . then buying

in 2000 and selling in 2002 would have returned money . but it did not . for the most part i agree with you . yet there are a few things i disagree on . 1 obviously predicabilty of returns is not true

as for hegde funds .we should ask ourselves this . are they true hedge funds or are they just hedged trades . there is a difference and i suspect more of the latter . the money going there is still at risk . and some of what they are doing is fairly short term trading .

limited risk yes but not truelly what they imply which is hedging ones portfolio . in the end it is just speculation with a new name .

my real question is this . i do not know what this subject is , lol

category based ranking is best ??? for what ??

I agree that in the presence of “predictability gap”, buy-and-hold portfolios of stocks, bonds and European call options cannot approximate the optimal CE arbitrarily well, even as the number of options increases without bound. A natural extension is to include more complex derivatives, perhaps with path dependencies such as knock-out or average-rate options. This gap depends on the investor’s preferences as well as the parameters of the stock-price process. If the gap is small, the buy-and-hold portfolio may well be the optimal one even in the presence of predictable stock returns. Transaction costs as a percentage of initial capital would be higher if the stock returns are predictable. This should be true in general for other mean-reverting stock-price processes (congestion). If the stock price process displays some type of persistence in trend or momentum, a different class of derivatives mght be more appropriate.

The natural question to ask is how significant is this predictibility gap?

rgds, Pal

Midas Value

i would think that the predictability gap would vary from time to

time . and by measuring the gap we would find the oppurtunity .

at times the gap would be huge , other times very small .

when its small the stock price wold most likely be near the end

of a long trend . my thinking anyways .