Gain/loss under CDS position

CFA Level III Fixed Income
#1

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Kim buys $10,000,000 notional value of protection using the CDX contract. Kim’s view
turns out to be correct and after 12 months the CDS spread on the HY CDX contract
has doubled and the contract’s spread duration is 3.77.

I would have solved it like this:
buy protection/short risk position: (-change in spread ) x effspreaddur x notional = -3,50 x 3,77 x 10mn = 1319500
Because you buy protection, you also need to pay the coupon of 5% x notional = 500k
final answer: gain 1319500 - 500k

Turns out, this is not correct, as you need to compute the change in CDS price… but, why is my method not correct? This IS how you compute a long/short position in such a case (by using the a.m. formula I used, that is).

Many thanks!

#2

This reading is completely fouled up. Even some of their corrections (in the errata) are fouled up.

The correct formula for the price is:

CDS\ price = (CDS\ Spread - Fixed\ Coupon) \times EffSpreadDur_{CDS} \times Notional

(Note how this is consistent with Exhibit 26, one of the few things in this reading that’s correct.)

So, you buy the CDS today for:

CDS\ price = (3.5\% - 5.0\%) \times 4.66 \times \$10\ million = -\$699,000

(Note that this means that you receive \$699,000 today.)

One year from today you sell it for:

CDS\ price = (7.0\% - 5.0\%) \times 3.77 \times \$10\ million = \$754,000

Of course, you paid 5\% \times \$10\ million = \$500,000 as a coupon payment, so your gain is:

\$699,000 + \$754,000 - \$500,000 = \$953,000

As I say, that reading’s completely botched.

1 Like
#3

Thank you so much, and, you are right… such a reading :frowning:

#4

Was that the answer they got?

#5

Same as you, of course :slight_smile:
Kim buys $10,000,000 notional value of protection using the CDX contract. Kim’s view turns out to be correct and after 12 months the CDS spread on the HY CDX contract has doubled and the contract’s spread duration is 3.77.

The fund is buying protection and therefore needs to pay the fixed coupon of 0.05 × $10,000,000 = $500,000.

|Initial CDS Price|= 1 + [(Fixed coupon – CDS spread) × Spread duration]|
||= 1 + [(0.05 – 0.035) × 4.66]|
||= 1.0699|

The CDS price after 12 months when the CDS spread has doubled to 700 bps and the spread duration has fallen to 3.77 is calculated as:

|CDS price in 12 months|= 1 + [(0.05 – 0.07) × 3.77]|
||= 0.9246|

Because the fund has bought protection, it is a short credit risk, and profits as CDS prices fall. Hence, the profit/loss from changes in the CDS price = (1.0699 – 0.9246) × $10,000,000 = $1,453,000.

Total return, including the coupon outflow = $1,453,000 − $500,000 = $953,000.

However, when I see these questions, I always tend to go first for the long-short method, i.e. applying the formula to calculate the value of the long-short position:(-change in spread ) x effspreaddur x notional.
Is there any way to know when it is better to calculate the change in price, versus the value of the long/short position? Do they specifically need to say smth about long-short, or specifically state, that, for instance, spreads on 5y decrease, while the ones on 10y increase?
Otherwise, you should rather go for computing the changes in price?

#6

I think the shorter formula is used only when there is no change in effective spread duration.
In this question, the duration has changed and needs to be solved the longer way

#7

Got this queation from reddit. And I have the exactly same one. Can you pls help…

CDS price = 1 + ([CDS coupon - CDS spread] * ESD)

Using fake numbers:

.9 = 1 + ([.05 - .07] * 5)

So the price of this HY CDS will be 90% of par, hence the buyer of the CDS pays the seller 10% of the NP.

Now if the spread widens from .07 to .09:

.8 = 1 + ([.05 - .09] * 5)

The price has fallen to 80% of par

This is confusing to me because the buyer of the CDS gains when spreads widen, but looking at the price one would naively assume that they lost.

The logic I am using to explain this discrepancy in my head, using the example above is:

The buyer initially paid the seller 10% of NP to buy the CDS. In order to unwind the trade they would have to sell the CDS. Since spreads widened they’d collect 20% upfront payment, leaving them with net 10% of NP as profit.

Is this is the correct way to think about this?

#8

Yes, when CDS spread widens, buyer gains.
This reduces the price of the security and benefits CDS buyer because he is short the credit quality. That’s the mindmap you need to follow.
Another way to present your answer is,

  1. Since spread duration is unchanged, just calculate (New Spread - Old Spread) x SD and then profit can be calculated.
  2. CDS coupon can be shown separately here anyways since it’s standardized.
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#9

I’m confused about this. If CDS price is equal to this:
CDS price = (CDS Spread - Fixed Coupon) x EffSpread x Notional

and you are saying it is consistent with exhibit 26, are you saying that the:
CDS Price = Upfront Premium?

Exhibit 26 gives the upfront premium in the second column. That seems odd to me that the CDS price is equal to the upfront premium and I cannot wrap my head around it.

To elaborate further, if we look at example 27. If you look near the end of solution, the CFA text uses:

10 year CDS price per 100 = [1 + ((1 - 1.75%) x 8.68)] = 93.4
9 year CDS price per 100 = [1 + ((1 - 1.66%) x 7.91)] = 94.78

But S2000 is saying the CDS prices are:
10 year CDS price per 100 = [(1 - 1.75%) x 8.68)] = -6.51
9 year CDS per price 100 = [(1 - 1.66%) x 7.91)] = -5.22?

and these negative CDS prices are equal to the upfront premium? How can we have negative CDS prices? What am I missing because I am sooooooooo confused. Please help S2000.