Instantaneous Forward Rates

Relative value analysis (RVA) is an important subject for the debt market, as it allows comparing different FI and MM instruments (bonds, CDS, swaps, etc.) with one another and making respective trading decisions. In this series of articles you will find the description of its purpose and application.
Why is this value analysis called “relative”?
The answer is: because the instruments are evaluated in relation to a benchmark bond or curve to determine, whether they are traded “rich” or “cheap”.
A direct comparison to a benchmark bond is possible when we are looking at two instruments that have the same maturity or duration.
But an often situation is that there may be no obvious benchmark to compare, therefore a yield curve is used.
It is important to keep in mind that the curve itself is not a financial product or instrument, but an interpolation or regression analysis tool.

That said, RVA can be carried out using 3 sets of measures:

1) Set 1:

• Yield (YTM / YTP / YTC / Current Yield*);

• I-spread (interpolated spread);

• Z-spread (zero-volatility spread) / C-spread;

• ASW-spread (asset swap spread).

2) Set 2:

• Tenor (time to maturity);

• Macaulay duration (weighted average maturity of cash flows);

• Modified duration (percentage derivative of the price with respect to changes in yield);

• Effective duration (a discrete measure of a bond’s price sensitivity to changes in yield – used for bonds with embedded options, as it captures the additional convexity imposed by the value of the option).

3) Set 3:

• Credit ratings.

Normally these parameters are used as metrics to construct a scatter chart with Set 1 on the vertical Y-axis and sets 2 & 3 on the horizontal X-axis.
Thus it is possible to visualize different yield curves and plot various instruments in a scatter format to further perform spread analysis.
A sample chart used for RVA is displayed below.

* Current yield can be used in case of a floating rate note (FRN).