I believe many of you quant guys have done back testing at some stage. I just got a project to evalute our asset allocation advise. Can someone shed some light on the approach, how to maintain the integrity of the presentation? Any input is much appreciated.

In my mind, backtesting has to do with something like this “what happened in the past when, in response to X event, I would have done Y action.” Or “Sell in May and go away” returns 15% more than buy’n’hold in the last 50 years, etc. In other words, it’s not really an asset allocation thing but an event thing that you backtest. That being said, in context of asset allocation, I would argue that mean variance optimization is basically just backtesting a particular asset mix over whatever period of time. The results will tell you the likely returns and the expected volatility. So that is a backtest.

There are a few ways to do it. The simplest is just looking at how an asset allocation (or allocation model, where the model tells you what allocation to use in various circumstances) would have performed on actual historical data. This is often the first one used for a new allocation, since if you had the allocation in place all the time, you’d already have the answer as to how it would have performed in the actual performance data. Another approach is to use the allocation model in several different historical periods, bull markets, bear markets, inflationary periods, etc. This might be a kind of scenario analysis. Another approach is to use different country markets in order to generalize beyond something like US markets. Of course, that assumes that the allocation model isn’t already a global model that includes these markets. Another set of approaches is to look at the statistical properties of historical markets (things like means and variances, but potentially including momentum, and other stuff) and try to reproduce them using a Monte Carlo approach. This has the advantage of recognizing that the way things have evolved historically might not be the only way things could have evolved. You are assuming that any specific asset history is influenced by a lot of random stuff, but that the overall level of randomnesss to growth/decline is somehow constant or at least predictable. There are a bunch of ways to do the statistical properties. If you assume that only means and variances/std deviations matter, MVO pretty much gives you the same result, as virgin said. If you think that other things influence the evolution of assets, then you may need to do something more like monte carlo. You can do something called bootstrapping, which simply assumes that the distribution of asset returns is representative of how the asset behaves, and essentially choose daily returns in a simulation by randomly choosing a historical day and the return from that day. Or you can chop up specific periods of time and reassemble them. So lots of choices, some more similar than others. I’m less familiar with the software out there to do it.

bchadwick Wrote: > Another set of approaches is to look at the > statistical properties of historical markets > (things like means and variances, but potentially > including momentum, and other stuff) and try to > reproduce them using a Monte Carlo approach. How would you suggest approaching Monte Carlo simulation for n assets? > I’m less familiar with the software out there to > do it. Matlab

maratikus Wrote: ------------------------------------------------------- > bchadwick Wrote: > > Another set of approaches is to look at the > > statistical properties of historical markets > > (things like means and variances, but > potentially > > including momentum, and other stuff) and try to > > reproduce them using a Monte Carlo approach. > > How would you suggest approaching Monte Carlo > simulation for n assets? Each asset has its own process, perhaps influenced by common factors. > > > I’m less familiar with the software out there > to > > do it. > > Matlab Certainly no reason one couldn’t use Matlab.

you can do monte carlo in excel

bchadwick Wrote: ------------------------------------------------------- > maratikus Wrote: > -------------------------------------------------- > ----- > > bchadwick Wrote: > > > Another set of approaches is to look at the > > > statistical properties of historical markets > > > (things like means and variances, but > > potentially > > > including momentum, and other stuff) and try > to > > > reproduce them using a Monte Carlo approach. > > > > > How would you suggest approaching Monte Carlo > > simulation for n assets? > > Each asset has its own process, perhaps influenced > by common factors. i agree but it’s still challenging …