Interactive Data Fixed Income Analytics-fixed income portfolio and credit risk analytics

The following article is reprinted from the March, 1998 issue of On the Edge,
the Interactive Data Fixed Income Analytics bimonthly newsletter.

Portfolio Optimization:
Dealing with Option Risk and Prepayment Model Risk

Wesley Phoa, Ph.D.
President of Research

The BondEdge Total Return Optimizer is a powerful tool for formulating portfolio strategy and for generating specific trade ideas. As explained in the February 1998 issue of On The Edge, the Optimizer has a distinctive feature which ensures that it generates meaningful results for bonds with option risk, such as callable bonds and mortgage-backed securities. This is the ability to specify, not just a single market scenario, but a range of scenarios, each weighted by an appropriate probability.

This is critical for investors evaluating option-embedded bonds. For example, suppose we are working with a universe which contains a callable bond. If we run the Optimizer with a single scenario, it will tend to gravitate towards this bond because of its higher yield. If we instead use a range of scenarios, the bond will seem less attractive because of its negative convexity, and will have a significantly lower weight (or perhaps even zero weight) in an optimal portfolio.

There are two approaches to entering a range of scenarios: one can use either (a) an objective probability distribution based on historical volatilities or implied volatilities of exchange-traded options, or (b) a subjective probability distribution based on the investor's own judgment. For example, if an investor has a specific view that volatility will be low, or that the market will range trade, the Optimizer can be instructed to take this into account

When dealing with mortgage-backed securities, a further issue arises. The BondEdge prepayment model measures the option risk of these securities by estimating how sensitive prepayments will be to shifts in interest rates. But no prepayment model will be perfectly accurate - every prepayment model is subject to model risk, i.e. the risk that borrowers' behavior will not conform to the assumptions made by the model. Thus any model is liable to mis-estimate the relationship between interest rates and security returns. In the case of a good model, the errors will be moderate and unbiased; but they will always be there. We hope this update has been useful. If you have any questions or would like more information about the PART system, please contact your Interactive Data Fixed Income Analytics Representative.

But if the model itself is prone to error - model risk - how valid is it to rely on the model when searching for optimal portfolios? The answer is: the optimization process is still valid for mortgage-backed securities, but one must be more careful interpreting the results. The degree of confidence is different.

If one runs the Optimizer on a universe of Treasury bonds, one can be certain that the portfolio it finds will be the optimal one (under the given assumptions, of course). If one includes MBS in the universe, it is merely probable that the portfolio found by the Optimizer is optimal, or nearly optimal. One cannot find the "true" optimal portfolio, because it is impossible to forecast borrowers' behavior with perfect accuracy; the best one can do is to generate a "best estimate" of what the optimal portfolio should look like.

Another way of putting this is: you will have as much faith in the results of the Optimizer as you do in the prepayment model itself. If the model is good at estimating the observed responsiveness of MBS prices to interest rate shifts the criterion which Interactive Data Fixed Income Analytics applies to all its prepayment models - then the Optimizer will produce useful results.

Actually, the degree of confidence you should have in the results of the Optimizer depends on (a) how much confidence you have in the model, and (b) how sensitive the specific securities are to changes in the model assumptions. For example, even if one believes that prepayment model risk is in general very great, one would still feel confident using the Optimizer to manage PAC tranches, because their performance is quite insensitive to model risk.

How can you tell in practice how much confidence you should have in the results generated by the Optimizer? BondEdge provides a straightforward method: measure the prepayment model risk of the securities in the universe, using the "Prepayment Uncertainty" measure in the "Advanced Risk Measures" report. If the securities have moderate prepayment uncertainty, it is safe to rely on the Optimizer.

For example, suppose the original portfolio has a forecast return of 5.00% and the optimal portfolio has a forecast return of 6.00%; and suppose that both portfolios have a prepayment uncertainty measure of 0.25. This means that a 10% bias in prepayment estimates has a 25 bp impact on returns.

Then one can be quite confident that the optimal portfolio really is an improvement on the original one, since it would take a model bias of at least 40% to eliminate the predicted outperformance of 100 bp. In fact, the model bias would probably have to be significantly greater than this, since to some extent a bias in the model will affect the original and optimal portfolios in the same direction.

This is actually an instance of a general rule: do not take the results of the Optimizer for granted, but always analyze an optimal portfolio in detail to identify any specific risks which you may have overlooked when setting up the original problem.

The Optimizer can usually provide very useful guidance for investors managing portfolios of pass-throughs, PAC, TAC and most sequential tranches from CMO deals, and senior tranches from ABS deals. More volatile CMO tranches, such as principal-only strips, support tranches and (especially) interest-only strips, have exceptionally high exposure to prepayment model risk, as indicated by their high "Prepayment Uncertainty" measures. These kinds of securities are usually best traded on the basis of specific views about prepayments.