Question

1. We are living in interesting times.  Over the past 2 weeks, the S&P 500 Index has dropped over 10%.  At the same time, the short-end of the U.S. Treasury yield curve is approaching zero and long-dated yields are at all-time lows. Please evaluate the dynamics of this situation.  If the risk-free rate is falling, why aren’t asset prices increasing?  How would you describe the flow of funds and the direction of causality?  What does CAPM say about equity beta (β) in the current environment?  What predictions can you make based upon the current U.S. Treasury yield curve?

Answer 1

From the black sholes equation for implied volatility:

C = SN (d1) – N (d2) Ke -rt

Where,

• C is the Option Premium
• S is the price of the stock
• K is the Strike Price
• r is the risk-free rate
• t is the time to maturity
• e is the exponential term

Direction of Causality:

It can be seen that as the risk free rate declines, the implied volatility will increase.

Asset Prices:

As the risk free rates suggest the volatility has increased in the market and the S&P 500 has registered a 10% fall in last two weeks, the situation is that the equity instruments are being short by investors and the Treasury bonds are long by the investors. since the equity assets are being short therefore the asset prices are not increasing.

Predictions made on current US yield curve:

Since the treasury bond demand is rising as a result of risk averse investors moving from more risky equity investments to less risky bond investments, the price of bonds increase in the short term. As the prices increase for the bonds and Yield is inversely proportional to the price increase of the bonds, the yield rates for short term treasury bonds fall.

As investors migrate towards the bonds from the equity investments the , treasury curve changes for the longer term bonds as well as this implies more trust on payment by government on its debt. Therefore, the prices of long term bonds also increase and hence it casuses the long term bond yields also to lower.

There could be some major event in the corporate world which can cause the volatility to increase such as a major scam/meltdown/epidemic etc. The effect will be that government will work with corporates to decrease the effect on volatility

CAPM Beta:

Beta coefficient(β)=Covariance(Re​,Rm​)​/Variance(Rm​)

where:Re​=the return on an individual stock,

Rm=the return on the overall market,

Covariance=how changes in a stock’s returns arerelated to changes in the market’s returns,

Variance=how far the market’s data points spreadout from their average value​

As the risk increases, the denominator variance of market increases. Since Beta is constant, the covariance of equity investment and market also increase.

Therefore the higher the Beta, the more equity return is required to compensate for the high volatility of the stock. Only investors with high risk appetite would go for instruments with high Beta value. In times of volatility, the stocks with high beta value have the maximum change in their value and in the current scenario will cause relatively more loss to the investors than compared with stocks of lower beta value.

Also, stocks with high leverage will have more Beta value and hence would cause more loss for investors in such a scenario than compared with stocks not having much debt.