Investing Based on OAS or Carry?

Some Thoughts on Investing in Mortgage Derivatives
by Yong Liu, Principal, Structured Portfolio Management LLC*

As we approach an environment of slower prepayments, murmurs of an alternative carry trade strategy begin: buy discount trust IOs and buy back the duration through investing in treasuries or swaps.

The argument is that both IOs and treasuries/swaps have positive carry. While OAS for IOs is at a tight level, this strategy is contradictory to what we understand about OAS. We can be relatively certain that we will make the excess return of the OAS for the portfolio. We should invest confidently when the OAS is wide and not so confidently when OAS is tight. We have been exposed to this strategy before the LTCM crisis when the spread was quite tight. It is easy to be misled into levering up the equity to do this type of trade.

What is wrong with this strategy? Why not lever up and feel confident with that strategy? What should we expect of the excess return? The short answer is that the carry trade idea, besides being a marketing tool for dealers, is simply wrong. It is the equivalent to betting on the realized volatility being lower than the implied volatility of the option embedded in the IOs during the holding period. Levering up will make the portfolio susceptible to even greater exposure to the contrary of the volatility bet. The expected excess return is always the OAS of the portfolio. The long answer requires us to rethink the fundamentals of asset pricing theory as well as the source of OAS.

Fundamental Asset pricing theory (1) taught us that there is no free lunch; any excess return over a risk free rate is a premium for some sort of risk. OAS is no exception.

A typical method for the OAS calculation is to find the excess spread after adjusting for interest rate movement; one accomplishes this by Monte Carlo simulation of a risk-free interest rate model and calculating the excess spread that can accommodate the price of the bond. In this simulation, a prepayment model that maps an interest rate path to prepayment speeds is used. In other words, the OAS is the expected excess return for the mortgage bond after hedging out interest rate risk. Since the interest rate simulation is performed in a risk-neutral universe, it is important to note that the OAS is calculated after hedging out the interest rate risk.

The excess return of a portfolio is expected to be a value-weighted average of the OAS of each individual bond in the portfolio. It is as if every bond in the portfolio has excess return of OAS all the time. However, we know that this is not the case. Basic asset pricing theory states that one can go to a risk neutral universe to price a security if the risk can be hedged. This is done through the Girsanov theorem (1). The Girsanov theorem says that when dealing with a portfolio of bonds for the purpose of the portfolio, one can think and operate in the risk neutral universe for each bond as if we can assume excess return of the OAS for each bond, all the time.

For example, for a portfolio consisting of current negative carry IOs and treasuries, the OAS of the portfolio will partly come from the carry of the hedge. Consider another example: hedging the slope risk of inverse IOs by shorting the two year and going long the ten year. The hedging securities have negative carry, while the OAS of the portfolio will come partly from the current carry of the inverse IO. In reality the hedging security and the IOs will compensate each other so that the portfolio always has an excess return of the OAS that is the value-weighted average of each bond in the portfolio.

As we mentioned before, the OAS is not a free lunch for a mortgage investor. We can make an intelligent guess that OAS is a risk premium for some sort of risk that cannot be hedged. Actually it is the risk premium for prepayment uncertainty, or the market’s ability to model prepayments. There is always something in the future that we cannot predict. Gabaix [2] has demonstrated that mortgage OAS is strongly correlated to the ‘in-the-money’ concept of the whole mortgage market. When the whole market turns into discount, the OAS for IOs will diminish; one theory is that the need for taking prepayment risk will be less interesting to the market as a whole and thus less OAS for IOs. This seems to be the case right now.

The good thing about OAS-based investing is that the whole market switches gradually from premium to discount, thus the OAS is a slow moving number. An investor has plenty of time to adjust. Another source of OAS, is the market’s ability to model interest rate dynamics. The OAS and negative convexity of a bond have strong positive correlations. A bond with large negative convexity will fall off the cliff if a large movement occurs; while most interest rate models used by mortgage investors do not have a heavy tail distribution modeled in interest rate dynamics.

We have explained that OAS is the expected excess return. Next we need to understand what is wrong with the carry trade idea. The key to understanding is that the market does move around and we need to adjust constantly to maintain a zero duration portfolio. An IO with great carry is associated with large negative convexity, while the portfolio turns to have large negative convexity. This means the portfolio will be whipsawed by dynamic hedges due to market movement. This cuts into the carry of the portfolio. An IO can be thought of as shorting an option; a good proxy is 5x10 swaption. The P&L of hedging the portfolio dynamically with 10-year treasury for a month will be the difference of the realized volatility for the month and the implied volatility for one month option on a 10-year swap at the beginning of the month. Thus the carry trade is effectively a bet on realized volatility being lower than the implied volatility.

 

(1) Daffie, D. (2001) “Dynamic Asset Pricing Theory.” Third Edition, Princeton University Press

(2) Gabaix, X. and Krishnamurthy, A. and Vigneron, O. (2004) “Limit of Arbitrage: Theory and Evidence from the Mortgage-Backed Securities Market”. Technical Paper, MIT
http://econ-www.mit.edu/faculty/download_pdf.php?id=905