Could anyone please tell me if you have found Modern Portfolio Statistics to be a useful tool when choosing funds? And what is wrong with the following, which is what I seem to understand from what I have read:

1. The statistic R squared tells you how much of the movement of a fund can be explained by the movement of its underlying index, so a high value of R squared means that it is in effect an index tracker. In this situation the manager is adding little or no value, so the fund is only worth considering if the management fee is negligible (and of course if it is an asset that you want in your portfolio);

2. The statistic Alpha is a measure of the value that a manager has added, so a high Alpha would indicate a manager who is doing something more than simply tracking an index, the opposite message to that of a high R squared;

3. However, the method for calculating Alpha uses the value of Beta, which can only be calculated when R squared is high.

So: when a fund is not close to being an index tracker the figure for Alpha is meaningless. And when it is, all that a high Alpha can tell you is that it is tracking a good index, which is not what most of us expect a good manager to do.

### #2

I think you would look at it like this:

Beta is "how much does my investment move when 'the market' moves". Does it move more or less than the market.

For example a fund using gearing to invest in an index will move more than the index (more up in good times and more down in bad times). Its beta is high so you would think of it as high risk. A fund that invested 50/50 cash and index would see its NAV move less than the index, whether up or down, and you would say it was lower beta and lower risk.

Of course, beta has limitations because if the index you selected to be the benchmark is not really appropriate because it's not particularly well correlated with what the fund is doing from day to day or quarter to quarter or year on year, then an apparent high beta score, "ooh look it moved a lot more than the index" might be pretty much invalid.

Alpha is just: for a given beta score (the general level of risk in our "gearing" example), what is it actually performing at, compared to expectation?

So if we assume the risk free stuff like cash or gilts returns zero, to keep things simple; if the market goes up by 20% in excess of the return on cash or gilts and your beta score says you should get 1.5x that general market excess return because of taking more risk (e.g. smaller companies, or gearing), you might expect 30% gain. Then if you actually get 40% gain then you have positive "alpha". Or if you only get 25% gain despite taking a lot more risk than the index (for which you should have expected 30% gain), your alpha is negative. Try to avoid these managers

Two funds can have roughly the same performance in a year but with quite different levels of alpha. For example as above, if a fund got 41% but it was heavily geared so usually gets 2x the market, with a risk or beta level of 2, then you would have expected 40% in a 20% year for the market, so the alpha is pretty low. While if our fund from earlier that takes lower risks gets 40% when its beta only implied 30%, that's a high alpha. But any such analysis relies on the benchmark being a decent and fair comparator that's reasonably well correlated with what the fund is doing and measured over a decent time period so you can say what the beta is in the first place without getting garbage results.

The R-squared is a bit of regression analysis which says I have got some data on a scatter graph, how well does it fit my model (benchmark line). 100 is a great fit. Mathematically, looking at an rsquared score to compare real data against a model, anything that's lower than 100 is a less perfect fit and the data points don't fit on the line of expectation- but the number itself (e.g. 85) won't tell you whether there was a bias for the fund to be higher or lower than the best fit line.

A low score like 0 to 40 means the data points were really not very well correlated at all (e.g. you tried to use a global bond index as the benchmark for emerging market equities funds); the performance was statistically not-very-related to its benchmark.

In theory, if a fund has a great return, you should be able to use rsquared to see whether that was driven more by alpha or beta. BUT, if the r-squared value is very low, the figures can be pretty meaningless. An R-squared of 25 would imply only 25% of the movement of the fund's portfolio was explained by movements in the benchmark index, so the beta figure that had been derived is not going to be massively useful. So in that case, someone telling you they had calculated that fund to have a great alpha score, when actually the benchmark is not a particularly good one, means the idea that you found a great alpha in that fund is not too significant...

Beta is "how much does my investment move when 'the market' moves". Does it move more or less than the market.

For example a fund using gearing to invest in an index will move more than the index (more up in good times and more down in bad times). Its beta is high so you would think of it as high risk. A fund that invested 50/50 cash and index would see its NAV move less than the index, whether up or down, and you would say it was lower beta and lower risk.

Of course, beta has limitations because if the index you selected to be the benchmark is not really appropriate because it's not particularly well correlated with what the fund is doing from day to day or quarter to quarter or year on year, then an apparent high beta score, "ooh look it moved a lot more than the index" might be pretty much invalid.

Alpha is just: for a given beta score (the general level of risk in our "gearing" example), what is it actually performing at, compared to expectation?

So if we assume the risk free stuff like cash or gilts returns zero, to keep things simple; if the market goes up by 20% in excess of the return on cash or gilts and your beta score says you should get 1.5x that general market excess return because of taking more risk (e.g. smaller companies, or gearing), you might expect 30% gain. Then if you actually get 40% gain then you have positive "alpha". Or if you only get 25% gain despite taking a lot more risk than the index (for which you should have expected 30% gain), your alpha is negative. Try to avoid these managers

Two funds can have roughly the same performance in a year but with quite different levels of alpha. For example as above, if a fund got 41% but it was heavily geared so usually gets 2x the market, with a risk or beta level of 2, then you would have expected 40% in a 20% year for the market, so the alpha is pretty low. While if our fund from earlier that takes lower risks gets 40% when its beta only implied 30%, that's a high alpha. But any such analysis relies on the benchmark being a decent and fair comparator that's reasonably well correlated with what the fund is doing and measured over a decent time period so you can say what the beta is in the first place without getting garbage results.

The R-squared is a bit of regression analysis which says I have got some data on a scatter graph, how well does it fit my model (benchmark line). 100 is a great fit. Mathematically, looking at an rsquared score to compare real data against a model, anything that's lower than 100 is a less perfect fit and the data points don't fit on the line of expectation- but the number itself (e.g. 85) won't tell you whether there was a bias for the fund to be higher or lower than the best fit line.

A low score like 0 to 40 means the data points were really not very well correlated at all (e.g. you tried to use a global bond index as the benchmark for emerging market equities funds); the performance was statistically not-very-related to its benchmark.

In theory, if a fund has a great return, you should be able to use rsquared to see whether that was driven more by alpha or beta. BUT, if the r-squared value is very low, the figures can be pretty meaningless. An R-squared of 25 would imply only 25% of the movement of the fund's portfolio was explained by movements in the benchmark index, so the beta figure that had been derived is not going to be massively useful. So in that case, someone telling you they had calculated that fund to have a great alpha score, when actually the benchmark is not a particularly good one, means the idea that you found a great alpha in that fund is not too significant...