# Random portfolios for evaluating trading strategies

Random portfolios have the power to revolutionize fund management. You might think that means they must be esoteric and complex. You would be wrong — the idea is very simple. In order to have random portfolios you need a universe of assets and some set of constraints to impose on the portfolios. A set of random portfolios is a sample from the population of portfolios that obey all of the constraints. Figure 1 shows the sampling area in weights for a toy problem of three assets.

Volatility constraints random portfolios for evaluating trading strategies non-linear and hence the boundary corresponding to that constraint is non-linear. Allowable weights given some constraints. The most familiar form of random portfolios is the stock market dartboard game. Humans or monkeys throw darts to select one or a few assets. The selection via darts is then compared to some professional selection. This is fun, and almost a great approach, but has two failings. The first failing is that we only get to see if the professional outperforms one random selection.

To be truly informed we need to see on the order of a hundred or more random selections. The second failing is that the darts do not obey any constraints. But real funds do have constraints. Comparing a fund with constraints to random portfolios without constraints puts the fund at a disadvantage. There are random portfolios for evaluating trading strategies ways of using random portfolios to achieve performance measurement: We will see why performance measurement via benchmarks is inferior.

In the static method we generate a set of random portfolios that obey the constraints at the beginning of the time period, hold those portfolios throughout the time period, and find their returns for the period. The percentile of the fund is the percent of the random portfolios with larger returns. The convention in performance measurement is for good to be near the zeroth percentile and bad to be near the th percentile. Figure 2 is an example.

It shows the distribution of returns of the random portfolios random portfolios for evaluating trading strategies blueand the return of the fund in gold. In this case the fund did not perform very well. Static method of performance measurement.

This is very much like performance measurement with peer groups. In both cases we are random portfolios for evaluating trading strategies a single time period, and in both cases we are comparing our fund to a set of alternative possibilities.

There are some significant differences though — we highlight two. Ideally only funds with the same constraints would be used. On the other hand we want to have a lot of peers in order to get more precision. So there are opposing forces for small peer groups versus large peer groups. There is no such tension with random portfolios — we can generate as many random portfolios as we like.

This assumes that differences in skill dominate differences in luck. Such an assumption is unlikely to be justified. In particular if it is the case that no fund has skill or all the funds have equal skillrandom portfolios for evaluating trading strategies our fund is at the 10th percentile of luck — the measure contains no random portfolios for evaluating trading strategies at all.

Burns a expands on this argument. Surzdiscusses additional problems with peer groups. The static method for random portfolios is more informative than peer groups. But it is still rather generic information. Performance is — at root — about decisions. The idea of the shadowing method is to use random trades to mimic the decisions that the fund takes. This can give us a much clearer picture of the value of the decision process. An example is discussed in the performance measurement application page.

A fund is judged against a benchmark by comparing a series of returns from the fund with the corresponding returns for the benchmark. This method has a few problems. The major one is the time it takes to decide that a good fund really is better than the benchmark — it probably will take decades. The power of random portfolios for evaluating trading strategies tests in random portfolios for evaluating trading strategies ideal setting is given in Burns a — several years are required to get reasonable power even for exceptional skill.

But the reality is much worse than the ideal because the difficulty of beating a benchmark is not constant. If the most heavily weighted assets in the benchmark happen to perform relatively well, then it will be hard to beat the benchmark.

Conversely, if the most heavily weighted assets perform relatively poorly, then it will be easy to beat the benchmark. Kothari and Warner discuss this. In order to believe that the comparison is meaningful, we need to think that **random portfolios for evaluating trading strategies** fund managers — as a group — were poor for years, suddenly became good for three years and then went back to being poor.

Burns b discusses performance measurement in the slightly different setting of random portfolios for evaluating trading strategies the recommendations of market commentators.

Fund managers and potential fund managers face a number of problems when deciding on a trading strategy. Here we examine two:. Data snooping makes the strategies look better than they really are. To see why, suppose that you tried trading strategies that were completely random.

The one that performed best might look reasonably good. If similar models are being used in several companies to manage a lot of money, then a fund manager using those models is subject to dramatic moves in the market. This became evident to a lot of people in August Without a crisis it is hard to tell that this is happening. Trading strategies can be tested using the shadowing method discussed above.

There is one key difference between performance measurement and testing a trading strategy. When testing a trading strategy we want to do the shadowing process a number of times with different starting portfolios. This testing process reduces the effect of data snooping because there is a much stricter definition of random portfolios for evaluating trading strategies successful strategy. The fund manager is still vulnerable to changes in market behavior, but much less susceptible to wrong interpretations of the historical period.

Testing with random portfolios may be able to reduce herding because the technology makes it feasible to pick up more ephemeral signals. There **random portfolios for evaluating trading strategies** also a blog post about backtesting. Many mandates give the investment manager a benchmark and a maximum tracking error from the benchmark.

This is wasteful in several respects. In virtually all cases the investor can buy an index fund for the benchmark with very low management fees. If the manager does have the skill to consistently beat the benchmark, then that skill could be put to much better use.

A skilled fund manager should, in general, be able to achieve higher returns when the tracking error constraint is dropped. Assuming the investor has money in the index, that higher return of the unconstrained manager will be more valuable as well. All else being equal, it is better for the active fund to have a low correlation with the index. This turns out to be the same as a large tracking error.

That is, the rational thing would be to impose a minimum tracking error constraint rather than a maximum tracking error constraint. The reason there are maximum tracking error constraints is in order to have the illusion that we can see if the fund manager is outperforming or not.

Random portfolios work equally well for performance measurement no matter what tracking error there is. If you have a performance fee, it is not a good idea to have it relative to a benchmark.

As Figure 3 implies, that is mostly a bet between the fund manager and the investor on whether large caps will outperform. Skill will have very little to do with it. A more reasonable target would be the mean return of a set of random portfolios that obey the constraints of the fund.

We can use random portfolios to decide rationally what the constraint bounds should be. Constraints are habitually imposed with no sense of what is being gained and lost. Figure 4 shows an example analysis of constraints. The densities of realized utility over time are shown for a certain set of constraints gold and for those constraints plus a volatility constraint blue.

During the normal market times we will be fairly indifferent to the volatility constraint. However, during the poor market conditions of the volatility constraint was quite valuable. Effect of constraints in A number of additional uses of random random portfolios for evaluating trading strategies have been suggested and there is surely a large number of applications yet to be discovered. Here we discuss a few additional uses.

Random portfolios provide a means of generating realistic portfolios that can be put through risk models in order to see how they perform. Risk models can be compared with each other, or individual models can be tested for weak spots. The correlation between predicted and realized volatility across a large number of random portfolios was computed. Correlation of predicted and realized volatility. Random portfolios can be used in pretty much all quantitative exercises involving portfolios.

A list of some of the uses is in the quant research applications page.

Active asset management has been under attack during the past several months. Over a career, one may have the opportunity to work with dozens of portfolio managers and there are some that **random portfolios for evaluating trading strategies** us that they have found genuine sources of alpha and have a real skill. Unfortunately for every one of these portfolio managers, there are nine other guys.

The other guy, you know what I mean? Despite all the flamboyance, this guy really has no idea what he is doing. He might as well be rolling a pair of dice to decide what securities to buy and sell.

One alternative it to understand how well random portfolios for evaluating trading strategies performs when compared with strategies that have the same constraints that he is required by risk to stay within, but have randomly constructed trading rules. We give a demonstration on how to design a random portfolio based performance metric below in the context of a simplified example. All the while the trader regularly reminds you that he is crushing your credit, FX, and swaps teams, is carrying your firm, and now needs you to double his AUM.

How can we evaluate the performance of this PM before deciding whether or not to ramp up his capital? First, we select a random subset of 10 stocks from the index and generate a normalized vector of weights whose components are i. We then compute the simple returns of each stock and take a weighted sum to find the daily returns of the portfolio. From this, we estimate random portfolios for evaluating trading strategies annualized return, volatility, and Sharpe ratio using a day lookback window on a rolling basis and store the resulting Sharpe ratio time series.

Then we repeat this process 10, times. Finally, we compute the mean and standard deviation of the set of 10, points associated with each day in the six year holding period and plot the mean series in the below figure in blue and the 2 standard deviation series on both sides of the mean in grey.

The first thing that we note is that our random portfolios did quite well. They had a respectable Sharpe Ratio above 1 for more than half the trading period and seldom had negative year-on-year returns. However, we also note that the distance between the upper and lower grey error curves is quite small.

It random portfolios for evaluating trading strategies from being nearly zero to around 0. This seems to make things quite difficult for the trader to distinguish himself as it seems all trading strategies appear to be closely related to one another. Let us look into a few further descriptive statistics and performance measures of this trading strategies but now only considering the full six year time window and varying the number of securities that a trader is allowed to hold. First, we take the last point of the cumulative return series of each random portfolio and annualize it.

Notice how as we increase the number of securities, the variance of the expected annualized return distribution decreases. Specifically, we compute the standard deviation of the returns of each random portfolio on a rolling window and then annualize by multiplying by a factor of and then repeat for varying numbers of securities and plot the results below.

Note that the distributions are skewed to the right. Note how these distributions also localize as the number of stocks selected increases which gives a demonstration of the diversification benefits of a larger portfolio. Dividing the annualized return by the volatility in each of the two above examples, we plot the distribution of Sharpe ratios for each simulation. Also, the right skew in the random portfolios for evaluating trading strategies distributions creates a left half skew in the Sharpe Ratio distributions.

From this plot, we can see that is it quite difficult to construct a poorly performing strategy within our model constraints even if one set out to do so from the onset. Specifically, the majority of Sharpe ratios are within the respectable range of 0.

Finally, we compute the maximum peak-to-trough drawdown of random portfolios for evaluating trading strategies of our simulated strategies and plot the results below. The above is a simplified example that would not be reasonable to implement in practice. This allows for the construction of one additional performance random portfolios for evaluating trading strategies on which to evaluate the performance of the strategy.

You are commenting using your WordPress. You are commenting using your Twitter account. You are commenting using your Facebook account. Notify me of new comments via email. May 27, Author: An All-Star Stock Trader? A Random Portfolio Monte Carlo Simulation First, we select a random subset of 10 stocks from the index and generate a normalized vector of weights whose components are i.

Limitations, Extensions, and Conclusions The above is a simplified example that would not be reasonable to implement in practice. I gotta favorite this web site it seems very beneficial very beneficial Like Like. Leave a Reply Cancel reply Enter your comment here Fill in your details below or click an icon to log in: Email required Address never made public.

They even appear to be applying exactly the same rules but in fact are not. I think I will have a carefull look into it before taking any further. Im interested in laying system especially under 4 and if it works.