BB Credit using market cap volatility, solving for Distance to Default
(d2 in Black Scholes)
The input for a stochastic analysis of BB credit is the volatility of the Russell 2000 index, specifically the one year realized volatility (240 N):
The Russell 2000 volatility is transformed via simultaneous equation into asset volatility, using the equity value for the R2000 and the debt o the R2000 firms, the volatility of the market cap (debt and equity - “Vola” below):
Vole = [N(d1) X V X Vola] / E
The asset volatility, Vola, derived:
Asset Vol of the Russell 2000 is scatterplot to BB spreads, shows the deeper insight of a stochastic analysis.
While the above scatter of log of Russell 2000 levels versus log of BB spread suggests that BB spreads might even be wide and may tighten, Russell 2000 asset vol scatter to BB spread shows the opposite.:
The asset volitility is the “sigmaa”“, or vol of the underlying, in a standard Black Scholes formula to find the d2. We do not solve for price, just 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) 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 often called when using a Merton formula the “distance to default”, or D2D. D2D is plotted over time. While the Russell 2000 has sold off of late, the D2D of the Russell 2000 has crashed and has lost 1/2 the peak value during the low sub 10% volatility period before Feb 2018 this year. Currently D2D for the BB credit using Russell 2000 is 3.9822406 and a year ago D2D was 6.913565 :
The above D2D is scatterplot against BB spread.
It is obvious that BB spread currently ( December 22 2018 ) can explode upwards, doubling towards 4% to 4.5%. Since this is based upon volatility the characteristics of vol changes, long dated vol, it will change via regime shifts of jumps up or down. Volatility does not move in a discrete fashion like Russell 2000 price and likewise credit spreads which we are showing are pricing volatility will move in regime shifts.
A closeup of the above larger scale scatter is given, which gives greater detail:
It is very likely that BB credit spreads, unless long dated volatility of the Russell 2000 drops again to levels of 2017, will surge wider. This may surprise as it can happen while the Russell 2000 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.
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