AA credit analysis using market cap volatility, solving for Distance to Default
(d2 in Black Scholes)
## [1] "SP500"
## [1] "BAMLC0A2CAA"
The main input for a stochastic analysis of AA credit is the volatility of the SP500, specifically the SP500 one year realized volatility (240 N):
The SP 500 volatility is transformed via simultaneous equation into the asset volatility, using the equity value for the SP500 and the debt to arrive at a market cap (Vola below) or 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, makes for insight of 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 that AA spreads are very tight (rich) despite SP500 trading up the last few seassions:
The asset volitility is the sigmaa, or vol of the underlying Enterprise Value, in a standard Black Scholes formula used to calculate the d2. We do not solve for standard 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 3%). 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, the D2D of the SP500 has not traded up from the recent lows, and has lost more than 1/2 the peak value during the period of low sub 10% volatility before Feb 2018, when the first vol spike in SP500 occured. Note the D2D does not track the SP500 level, but the volatility increase in the SP500. Currently D2D for the AA credit is 5.358686 and a year ago D2D was 8.8487606 :
The above D2D is scatterplot against AA spread.
AA spread currently ( February 22 2019 ) can explode upwards, doubling towards 150 to 175, which this wider spread potential has not changed despite the uptrade in SP500 since December 2018. 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 which we are showing are pricing volatility will move, in the end, in response to regime shifts.
A closeup of the above larger scale scatter is given, which gives greater detail:
It is likely that AA credit spreads, unless long dated volatility of the SP500 drops again to 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.
