# Credit Analysis Models - Schweser - page 173 - Study Session 14

For number 8 , why is the total yield 0.14% when the risk free rate and credit spread is 0.15% and 0.13% respectively? Aren’t you supposed to add both to get the total yield?

Also, if someone could explain the inutition behind this statement, it would be very helpful:

“A long position in risky debt with a face value of K is analogous to a long position in a risk-free bond with the same face value K, plus a short position in a European put option on the assets of the company with a strike price equal to K”

Thanks guys.

The theory here is that an economic default is when the asset value of a company falls below the debt owed. In this case, the equity holders of the company are better off handing over the company assets to the debt holders instead of repaying the debt. Therefore the equity holders are long a put option on the assets of the company because they can put them to the debt holders. The debt is short this put option to the equity.

The coupon of a bond can, in a simple theoretical construct, be decomposed into a risk free rate plus a risky premium. This risky premium represents compensation for taking the on the risk of the debt (which is essentially represented by the short put option on the company assets as shown above).

So lets try to decontruct this. If i were a holder of a risky bond. It would be equal to a risk free bond plus a short put on the company’s assets.

Short put means you are selling the right to sell at a certain price (face value of debt). So if the asset value drops below the debt value, the put position portion (of the person who is holding the risky debt) will lose value (X - S is positive so the long gains and put seller loses). So the value of the riskyt debt will be "Risk free + (negative X - S). The value drops below the value of the risk free and it’s equal to the difference between the Exercise price and the asset price.

Let’s say the opposite happens: Now the Asset price is way higher than the exercise. So the person holding risky debt has a value equal to: Risk free + value of put. In this case, since th put is out of the money, the put seller wins, but since he sold this put before, the value of this put may drop since it is way out of the money. So if someone goes long the put, it would be very cheap. So the risky debt is very cheap even though assets are very high in value? Trying to understand this. So if the Assets value goes much higher, in theory this would mean that the value of this put option gets cheaper and cheaper to the point where the risk free debt almost equals the risky debt. To me this doesn’t make since. If I were a risky debt holder, the value of my risky debt should go up in value if the company’s assets go up in value.

Am I making sense here?

This is really about replicating cash flows. For example: I buy a 10yr risky bond with a 5% annual coupon for \$100 (face value). In 10 years, if the company has assets of at least \$100, I will get all my money back. If the company only has \$80 in assets in 10 years, I will only get \$80 and lose \$20. Let’s say instead I buy a 10yr risk free bond with a 2% annual coupon for \$100 (face value). Then I sell a put option on the company’s assets with a strike of \$100 for an annual premium of 3%. So I’ve now got \$100 invested and 5% coupon just like the risky bond above. In 10 years, my risk free bonds pay me back \$100 and if the company’s assets are worth \$100 or more the put is not exercised. If the company’s assets are worth \$80, the put is exercised and I lose \$20. Therefore, I’ve recreated the risky bond position by buying a risk free bond and selling a put option on the company’s assets.

Hey but what is reason behind the calculations mentioned by original poster for risky bond?

For number 8 , why is the total yield 0.14% when the risk free rate and credit spread is 0.15% and 0.13% respectively? Aren’t you supposed to add both to get the total yield?

I’m on the same page.

The similar question is on the page 165. In that question, the total yield is definately calculated as the sum of Risk Free and Credit Spread.

And one thing I’ve noticed is that, the Total Yield on the page 173 is completely the same to the oneson the page 165. This might be accidental, but I guess that is miss-printed…

Any thoughts on this?