# “Where is my money”: CDS Sensitivities, Spreads and PnL Calculations

Trading CDS I experienced something unexpected:

• A half year ago I sold protection on a single name at a spread of 190bp
• The coupon was 5% and the contract had a maturity of five years.
• Using Bloombergs CDSW function I noticed that the SpreadDV01 was ~480€
• I paid an upfront of ~141k (+ 4k accrueds)

A half year later:

• the CDS was quoted with a spread of 160bp. I thought "Great! Thats a profit of 14k€ (=30bp*480€) addional to my received premiums of 25,000€ (5%*0,5*1MM). So a total PnL of +39k"
• When I was validating the position I discovered that my position only gained ~2.6k on value (the upfront I would receive now is 143,6k) addtional to my collected premium of 25k

Besides how is this possible my questions are:

1. why the SpreadDV01 failed to predict my return on this position?
2. are other there tools used by practitioners to approximate the total PnL of a CDS position?

• Among other effects, a 1/2 year has passed between entering and exiting the position, so you can't use the initial SpreadDV01, which was computed for a 5 year remaining maturity. – Antoine Conze Jan 23 at 16:18

You would need to provide more details for an accurate PnL attribution. However, here are some additional points to consider that might help.

When you sold protection, you effectively became long the 5Yr synthetic debt of the reference entity at a credit spread of 190bps. Since the coupon is 5%, this would imply a 5Yr (at the coupon frequency of the premium payments) risk free rate of 3.1%. I assume that the reference entity and the sovereign where the company is domiciled is European given that you are quoting the spread dv01 in Euro terms. Also, the sovereign is probably a dicier sovereign given the high risk free rate (Greece, Italy?)

So as being long the debt, you would be correct that you should have benefitted from a tightening of the credit spread. However, since you did not benefit as much as you thought, there must have been an increase in the risk free interest rate of the sovereignty that the company was domiciled.

Another factor that may have impacted your PnL is the shape of the yield curve could have changed. While most long debt positions benefit from the concept of roll down in that yield curves tend to be positively sloped, the sovereign curve where your company is domiciled may have inverted in 4.5-5Yr maturity range and therefore your position would have been hurt by the roll down effect. (In the US, the curve had inverted at the 5Yr point recently).

Since the last 6 months had a lot of volatility and hence created some consternation among market participants, the liquidity, and hence the bid-ask spread of the reference credit and the sovereign may have widened which could have hurt your position.

A point that should have helped you is the convexity. Since you are long the debt, a big move in rates would have some convexity that would have improved your position beyond what you would have expected from the DVO1 prediction.

@AlRacoon was completely right by suspecting convexity for this issue. The Chart below shows the impact of the convexity in this trade very well.