AA Credit Analysis Based Upon SP500 Volatility, Solving for Distance to Default
(d2 in Black Scholes)
Most perceive credit as an ex post problem related to firm value with equity price bing the most important input. The recent recovery of SP500 levels has prompted buying in credit. While SP500 has not made new highs, credit spreads have returned to where they were before the SP500 sell off of 4th Q 2018.
However, the main input for a stochastic analysis of AA credit is the volatility of the SP500, we use the SP500 one year realized volatility (240 N):
The SP 500 volatility is transformed via simultaneous equation into asset volatility, or the volatility of the entire enterprise value, using the equity value for the SP500 and the debt to arrive at a market cap (“Vola” below), the volatility of the Enterprise Value (debt and equity) is derived:
Vole = [N(d1) X V X Vola] / E
The asset volatility derived:
Asset Vol of the SP500 is scatterplot to AA spreads, a stochastic analysis of credit.
While the above scatter of log of SP500 levels versus log of AA spread suggests that AA spreads might even be wide and may tighten further, SP500 asset vol scatter to AA spread shows AA spreads are tight (rich), despite SP500 trading back up towards all time highs:
The asset volitility is the sigmaa, or vol of the underlying Enterprise Value, in standard Black Scholes formula used to calculate the d2. We do not solve for a option price, just the d2, as the price asymtopes along the x axis, and while correct theorectical is of little use for trading and risk management.
The d2 formula is well known:
The d2 depicts in units of volatility years (Brownian scaling of time) showing how far the underlying credit is from default given the current asset volatility, for a certain time period (we use 5 years), and for a certain interest rate or rho (we use 2%). The d2 is called, when using a Merton credit formula, the “distance to default”, or D2D. D2D is plotted over time and while the SP500 has rallied back from recent lows and almost back to record highs, the D2D of the SP500 has not traded back up significantly from the recent lows, and has lost more than 60% of peak value during the period of low sub 10% volatility prior to Feb 2018, when the first SP500 vol spike occured. Note D2D does not track the SP500 level, but does track the volatility increase in the SP500 qualified somewhat by SP500 level.
Currently D2D for the AA credit is 5.5959888 and a year ago D2D was 6.9740064 :
D2D is scatterplot against AA spread.
AA spread currently ( March 27 2019 ) can move back upwards or widen, doubling towards 90 basis points. This wider spread potential has not changed despite the uptrade in SP500 since December 2018 as highr volatility was maintained.
Since d2d is based upon volatility and not SP500 market level, the characteristics of vol changes, in this case long dated realized vol, d2d will change via periodic regime shifts of jumps up or down.
Volatility does not move in a discrete fashion like SP500 price and likewise credit spreads, here AA credit, will price to volatility, in the end, in response to regime shifts of 2018.
A closeup of the above larger scale scatter:
It is likely that AA credit spreads, unless SP500 long dated volatility drops again to the levels of 2017, will go much wider. This may surprise, as it can widen while the SP500 is trading upwards.
It is obvious an ex post Altman or Graham Dodd type of credit analysis does little to anticipate or provide prescience for key credit spread moves.
