The backbone of our framework is the term structure of rates, including interest rates, real rates, swap rates (Libor), credit rates and volatility. Through principal components analysis we show that the market’s own modes of fluctuations of interest rates are nearly identical to the components of our term structure of interest rates. Essentially, our term structure model speaks the language of the markets.
Thus, the model requires the minimum number of components to explain all changes in interest rates. Five components can price all zero coupon treasuries within 2 basis points (bps) of market rates. More importantly, a different number of components can be used for risk management than for valuation without loss of generality. Exact pricing of all interest rate swaps that is provided by our methodology can be used for valuation of swap transactions.
The components of the term structure model represent weakly correlated sectors of the yield curve and can be used for structuring and risk measurement of portfolios. The first component, level, is associated with the duration of the portfolio. The second component, slope, is associated with the flattening/steepening structure and can be used to structure a barbell trade. The third component, bend, represents the exposure of a portfolio at the long and short ends relative to the middle of the curve and is used to structure a butterfly trade.
Valuation metrics along with the term structure durations for the identification of sources of alpha and risk are provided for all asset classes. We introduce the concept of partial yields as a way to decompose the contribution of different sectors to the yield of a portfolio. It is not reasonable to aggregate the yield of a security that has a high probability of default in a portfolio, since the resulting portfolio yield is not likely to be realized. Partial yield addresses this issue, by calculating the default probability and decomposing the yield into components that can be used to aggregate a portfolio’s yield. The valuation metrics and term structure durations along with linear programming provide tools for portfolio construction at the security level. This is also known as the bottom-up approach to portfolio construction and is useful for daily maintenance of a portfolio. Sector allocations and analysis of the portfolio’s mix of assets and durations and correlation among different asset classes are the subject of the top-down method of portfolio construction in fixed income. The two methods are complementary to each other; however, top-down is usually analyzed on a monthly or quarterly basis.
There is a step-by-step outline of building a spreadsheet based tool for designing new products or maintaining an existing portfolio. This tool provides the tracking error, marginal contribution to risk, and can be used for what-if analysis or to see how the portfolio would have performed during prior financial crises or how additions of new asset classes or sectors alter the risk profile of the portfolio. There is also a method to identify the structure of the competitive universe and design a product that could compete in that space.
We have provided detailed steps and formulation for the implementation of the framework that is outlined in the book. Many of the components can be built in spread-sheets; however, reliable and efficient analytics require the development of the necessary tools as separate programs. The benefits of such a framework and the potential performance improvements significantly outweigh its development costs.
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