Background:
Over the span of two weeks earlier this February the S&P index lost approximately 10% of its value. The correction might have been triggered by fears of inflation as investors suddenly became worried that tax cuts and an already overvalued stock market would require a faster than expected Fed intervention.
When we see market corrections (and we have seen plenty over the decades) we like to go back and analyze what our models were forecasting in terms of expected PL for certain securities.
In this short article we will look how Everysk would have forecasted the expected PL of a bullet corporate bond as a result of the SP500 10% drop earlier this February, a couple weeks before the event actually happened. We will use as an example a bond issued by Sprint Corporation maturing on 11/15/2028, with a 6.8755% coupon.
Common sense would have anticipated interest rates tightening and credit spreads widening as a result of the index drop. These effects have a negative correlation but it is difficult to forecast the net effect without a sophisticated system. Everysk uses sophisticated statistical methods to retain only relevant information about these propagation effects and to learn from them. We can’t nail exactly what will happened in the future (surprise!) but we can provide a robust projection that improves its estimates as more events are observed.
Before the correction:
On 01/10/18 (approximately 2 weeks before the correction) we were predicting the following propagated moves from a 10% up and down S&P shock to a selected rate and credit spread:
|
SP500 |
CMT 10YR |
B spreads |
|
+10% |
+12.25 bps |
-49.61 bps |
|
-10% |
-10.04 bps |
+48.81 bps |
Our calculation engine was expecting the 10 year constant maturity treasury rate to tighten approximately 10 basis points if the markets dropped 10%, i.e. going from 2.55% on that date to 2.45% (normal move). It also expected B spreads to widen by 48.81 basis points from a 10% equity correction, i.e. going from 3.45% on that date to 3.94% (normal move).
These rate and credit spread changes would have provided us with a forecasted PL of -3.37% for the Sprint bond. The details of how these risk factors are used in the bond simulation can be found in a companion article. Because we generate full distributions of risk factors (in fact 50000 correlated outcomes for rate and credit spreads), we were also able to provide a range around the -3.37% bond PL:
(*) Propagation from a -10% (left of x-axis) to +10% (right of x-axis) SP500 shocks to a bullet bond issued by Sprint Corporation. Yellow line is the expected PL as a percent of equity. Dashed blue lines are the extremes (5-percentiles) of the PL distribution. The -10% results are replicated below:
|
CORP:S 20281115 6.8755 |
|
|
Extreme positive(*) |
+6.95% |
|
Expectation |
-3.37% |
|
Extreme negative(*) |
-12.16% |
(*) best and worst 5-percentile of the PL distribution
How did these forecasted propagations fare with what actually was observed in the markets a couple weeks later? The table below shows the results side-by-side:
|
01/26/18 |
02/08/18 |
Observed PL from 01/26/18 to 02/08/18 |
Forecasted PL on 01/10/18 |
|
|
SPY |
284.16 |
255.45 |
-10% |
-10% |
|
Sprint bond |
104.5 |
100.5 |
-3.8% |
-3.37% |
We were expecting a slightly smaller PL impact on the Sprint bond due to a 10% drop in SP, compared to what was observed in the market, but the realized PL was well within our range of possible extreme events (-12.16% to +6.95%). The wide range of possible outcomes for the bond is indicative of its uncertainty (risk).
Summary:
We demonstrated in this short report how Everysk can reliably propagate macro shocks. We compared the observed price change of a corporate bond between 2 dates that the SP dropped 10%, with Everysk’s forecasted price change prior to that window. The observed price change, -3.8%, was a bit worst than our forecast of -3.37%, but well within our range of possible outcomes (-12.16% to +6.95%).
The example above shows how an equity index shock propagates to a bullet corporate bond. We can produce global stress tests that differ from a localized approach that stress tests securities via their pricing formulas, without propagation. We content our methodology is more relevant to buy side investors interested on big picture effects.
Additionally our methodology generalizes to shocks on any exogenous index, even when the index does not affect directly the securities via their pricing formula, such as an equity index above.