Risky debt/Risk free debt

[Kavita.bhangdia]

Hello everyone,
I had thought that I had sorted it out, but today I was reading the Merton model again but am completely lost with the difference between risky debt and risk free debt. Please can someone redefine it

Risky debt = riskfree debt-put option..

Please explain risky and risk free debt.

Thanks
Kavita

 

[brian.field]

are you familiar with the black - scholes equation?

C = S0N(d1) - K(e^(-rt))N(d2)?

The K(e(-rt)) is equivalent to a risk free zero (see that it is discoutned at the risk free rate?).

In the Merton Model, the K is replaced with the Face Value of the "risky" debt, or the face value of the firm's debt. But it is still transformed into risk free debt since it is discounted at the risk free rate, to be consistent with the B-S equation....and the underlying development.

 

[Mkaim]

Hello everyone,
I had thought that I had sorted it out, but today I was reading the Merton model again but am completely lost with the difference between risky debt and risk free debt. Please can someone redefine it

Risky debt = riskfree debt-put option..

Please explain risky and risk free debt.

Thanks
Kavita

Hi Kavita,

Let me attempt. First, the price of a risk free debt, holding all else constant, will be higher than a risky debt because it has no risk. So in order to back into the risky debt, you have to incorporate the risk into the risk free debt and you do that by subtracting the put price. In other words, the bondholders are effectively writing a put on the firm because they are confident that the price of the company stock will not fall below the face value of the debt. In Sum, the written put incorporates the risk into the risk free debt and effectively lowers the risk free debt value to a risky price. This is how it makes sense to me.

Just saw Brian's response. I agree with it, and it also links your question to another important concept (Black Scholes).

 

[Kavita.bhangdia]

In other words risky debt is just face value of debt. But risk free debt is Ke(-rt) is is present value of debt which we are calling risk free debt?
Thanks
Kavita

 

[Mkaim]

Current value for both. If you want the value of the firm's debt, equity, or assets today, you should use the PV or current market value if provided.

 

[ami44]

In other words risky debt is just face value of debt. But risk free debt is Ke(-rt) is is present value of debt which we are calling risk free debt?
Thanks
Kavita

Risk free debt is the value of the debt, if no risk of default would exist. Value means present value here. In the simplest case of the debt being a zero bond with face value K it's K * exp(-r*t), where r is the risk free zero rate at maturity t.

The value of the risky debt accounts for the possibility of default. For the investors the possibilty of default is bad, so the value of the risky debt is lower than for the risk free debt (from investors point of view).
The possibility of default can be imagined as a put issued by the investors to the company on its own stocks. If the stock falls below a certain threshold, the company does not have to pay back the investors. The value of this put can be calculated by BS. From the investors point of view the value of the risky debt is the value of the risk free debt minus the value of the put.

I hope that helped.

 

[Mkaim]

Risk free debt is the value of the debt, if no risk of default would exist. Value means present value here. In the simplest case of the debt being a zero bond with face value K it's K * exp(-r*t), where r is the risk free zero rate at maturity t.

The value of the risky debt accounts for the possibility of default. For the investors the possibilty of default is bad, so the value of the risky debt is lower than for the risk free debt (from investors point of view).
The possibility of default can be imagined as a put issued by the investors to the company on its own stocks. If the stock falls below a certain threshold, the company does not have to pay back the investors. The value of this put can be calculated by BS. From the investors point of view the value of the risky debt is the value of the risk free debt minus the value of the put.

I hope that helped.

Hi Ami,

Could you please let me know how your response is different from what's been mentioned above by me and @brian.field? I just want to make sure I'm not missing anything in my understanding.

 

[David Harper CFA FRM]

Awesome thread! Just in case a numerical example is helpful to match the commentary, here is screengrab of our merton model, where I just highlighted in orange the key terms mentioned above. The XLS is here if you want to explore further (this screengrab does not show the derivation of PD which is the second step in Merton, but PD is part of the XLS in the collapsed rows. It's easy to forget the Merton-type model is two steps: 1. option pricing to determine value of equity and debt, then 2. calculate PD based on estimated distance to default): http://trtl.bz/0413-merton-risky-debt

The key values in this illustration are:

• Firm (asset) value = $100.00
• Long-term debt matures in 5.0 years with par (aka, face) value of $80.00
• In merton, equity is a call option on the firm's assets with strike equal to par value of debt. Why? Because if shareholders "exercise" (i.e., pay off in full) the debt, they own the asset, just like an option holder owns the stock if she pays the strike. In this case, an option with a strike price of $80.00 on an asset priced at $100 (with volatility of 30%) has a value of $38.90, so equity value is 38.90. Due to balancing, risky debt value = asset value - equity value = $100 - 38.90 = $61.10
• But the other approach, as @Mkaim writes above is to assume "the written put incorporates the risk into the risk free debt and effectively lowers the risk free debt value to a risky price."
  • In this case, a put option (with strike = 80 on an asset priced at 100) has a value of $11.29
  • The value of risky debt = $72.39 - $11.29 put value = $61.10.
    
  • Put another way, as a bond investor, if you pay $61.10 plus you purchase a put option (which under the dubious Merton assumption represents protection against default) priced at $11.29, you've spent in total $72.39 for a portfolio that's (theoretically with assumptions) risk-free, so that should roughly match price for a risk free bond. Notice this price implies a spread of 3.391%. I hope that adds with color

 

[Kavita.bhangdia]

Thanks everyone for making it so clear...

Regards,
Kavita