0:00

[MUSIC]

Â So let's now look at how we go to the implementation and the estimation issue.

Â So as I said before, the strategic asset allocation undertaken by most

Â practitioners use a constrained mean-variance optimization technique,

Â and for that purpose, it will diversify in the simple case that we saw before,

Â between three asset classes, cash, stocks and bonds, fixed income.

Â But in a larger institution like, think about UBS, Credit Suisse,

Â JP Morgan, Goldman Sachs, we can have up to 20 asset classes.

Â 20 asset classes means we have to estimate about 20 mean returns for these classes,

Â and we have to estimate 490 parameters for the variance-covariance matrix,

Â so you see quite a large number of parameters to estimate.

Â I'll come to that point in a minute.

Â The portfolio weights are generally constrained to be equal to one,

Â no leverage, and to be positive, but that's not necessary,

Â some hedge funds may actually allow for short selling.

Â The mean variance and covariance estimates are to be for your horizon.

Â For instance, if I'm looking at my horizon up to my retirement,

Â this is going to be a relatively not very short horizon but

Â moderate horizon that is of about 10, 15 years.

Â If you're a young investor, you may have a 40-year ahead of you over

Â which you will do these optimizations, so the horizon is agent-specific.

Â Now, the question is, typically, remember we are still looking at

Â horizons of three to ten years, and over these horizons,

Â how do you estimate means, how do you estimate variances and covariances?

Â Now, if you look at variances and

Â covariances, in fact, they're much more easy to estimate.

Â If you have long sample data, a long history of data, and

Â you sample very frequently, let's say weekly or even daily,

Â you can get quite good estimates of the variance-covariance matrix for

Â these 20 asset classes, for instance.

Â Where the problems comes is when you have to estimate the mean, so

Â the mean will not be more precise.

Â So for instance, suppose I gave you 240 monthly observation

Â over a 20-year period, well, the mean that you would estimate for

Â each asset class, the mean return, would not be much more precise than the one that

Â you would get by simply taking the mean over the 20-year holding period.

Â And this has been acknowledged by many, many studies, in particular,

Â one of Goyal and Welch, who said it is so difficult to estimate the equity premium.

Â So the equity premium would be the expected return minus the risk-free rate,

Â and most models that are used would be unstable and spurious.

Â And how do banks, financial institutions here can bend this problem?

Â Well, they would do a mixture between using historical data and

Â estimates from the chief investment office practitioners, or somebody would sat

Â estimate domain return on the US stock market to be 10% next year.

Â Another guy would say 8%, some would say 7, and then you take an average between

Â all these forecasters to estimate your mean return on the SMP and

Â from the risk premium.

Â But, but, but this is not an easy task, and for many people,

Â the mean-variance optimization is actually called an error maximizer.

Â And let me explain why this is the case.

Â There was an interesting article in the journal of portfolio management, and

Â I'll just show you one graph where you have,

Â on the horizontal axis, the size of the error that you make.

Â It could be 0.05, 0.10, up to 0.20, and

Â the loss in term of the cash equivalent is on the y-axis above.

Â If you estimate means and covariances, you'll see that this loss is hardly

Â ever reaching 0.5%, never reaching 1%.

Â You'll see that as the error increases for

Â the mean, the cash equivalent loss can reach ten times more than

Â the one that you had when you were estimating the means and the covariances.

Â So in other words, it is much harder to estimate means and

Â risk premium, and it's much more costly to do a mistake at this level.

Â So let me try to give you some final words of caution.

Â 5:12

The result of mean-variance estimation is an efficient frontier.

Â You will know that.

Â You would position yourself on this efficient frontier by looking at

Â your utility or preference function, and the point that you would choose on

Â the efficient frontier corresponds to your risk appetite and

Â also gives you the weights that you would allocate into the different asset classes.

Â Well, while the theory is appealing,

Â we have seen that implementing the SAA is not easy, and primarily,

Â it's not easy because of estimating problems, and

Â these estimation problems are even more acute with the mean returns than

Â with estimating the parameters of the variance-covariance matrix.

Â So then, you may ask yourself, well, if we're so

Â much subject to estimation risk, how much should we care about SAA?

Â So typically, in a very well-known article in the Financial Analysts Journal,

Â a big debate over big confusion was settled.

Â And the confusion started with an article published in 1986 by Brinson,

Â where this author was perceived incorrectly by practitioners

Â as saying that 90% of the performance of a given strategy

Â originates from the strategic asset allocation component.

Â In fact, he never said that.

Â He said 90% of the variations in the time series of returns is due to the SAA.

Â And then in 2010, Ibbotson and his colleagues,

Â in a Financial Analysts Journal, settled the issue.

Â And they showed something which I think we should all know and

Â be aware of, which is that the time series of returns variation,

Â if you look at the two bars on the right,

Â are mostly due to market movements, which are uncontrollable.

Â In fact, 75% of the time series return variation is not manageable,

Â neither by the SAA nor by active management.

Â And the residual 25% of the time variation can

Â be explained in half, so 12.5% by the SAA and

Â 12.5% by Active Portfolio Management, so

Â be aware of this word of caution.

Â And to summarize, SAA plays a key role for passive investors, but on top of that,

Â many active investors will implement a so-called tactical asset allocation,

Â and that's something that you will see in the next lessons.

Â Thank you very much.

Â [SOUND]

Â