I hope somebody can help me with the understanding of the following problem. I am looking at interest rate sensitivity of a balance sheet which includes more interest-rate sensitive assets than liabilities. Part of the analysis are also off-balance sheet items, mainly interest rate swaps. To this balance sheet I then apply the following shock:
a) paralell shift +200bp --> this leads to an overall loss
b) shifting key rate durations each by +10bp (over the entire yield curve) --> this leads to an overall gain
Do you have any ideas why the effect of the upward shifts does not have the same direction (either loss or gain)? Could the swaps be the reason? Thank you in advance for any thoughts!
Let me know if I’m missing something but you’re basically doing a parallel shift of +200 for one scenario and then another parallel shift of +10bp for the other. “+10bp (over the entire yield curve)”
What are the duration and weights of each portfolio (assets/liabilities)? There are certain combinations of these parameters that can explain your scenario.
There’s got to be a convexity thing going on there.
Might take me a few minutes to remember what features make bonds more convex or not, coupon size, current key rate, maturity, embedded options, etc…
Floating rate bonds have very low durations and (I think) convexities, since they reset, whereas the fixed portion of a swap can have a high convexity if the term is long enough.
As spunboy said, stressing each key rate by the same amount is equivalent to a parallel shift, so you have a situation where depending on the magnitude of the parallel shift, a gain can turn into a loss. That seems a little strange.
I don’t think convexity can explain this, because convexity adjustment is a second order approximation which can refine the precision of your estimate, but won’t reverse the sign.
You can add or subtract duration using swaps, but again this is a static adjustment which would just modify the magnitude of the impact rather than create a sign reversal.
I’m thinking in order for you to observe this switch from gain to loss which is contingent on the magnitude of the shift, there needs to be an interest rate derivative as part of the portfolio - interest rate cap or floor or swaption. We need CSK’s help to tackle this fixed income conundrum.
If there’s enough duration on the liability side, a positive move in rates would give you a gain. Swaps complicate things but a 10bps move might not be enough to tilt the dynamics of the portfolio. However, a huge jump in rates (+200 is enormous) combined with receiver swaps might add enough to the liability side to give you a loss.
Not sure how in your explanation the impact of the receiver swap somehow kicks in when the shift is large, and overshadows the movement on the liability side while at the same time when the parallel shift is small, the impact of the swap in negligible?
This reference to asset side, liability side just confuses the argument. Why not focus on the duration of the total portfolio of assets and liabilties, on and off-balance sheet i.e. the duration gap. It’s either positive or negative or zero, with or without the convexity adjustment - doesn’t matter. Parallel yield curve shifts in the same direction have the same directional net impact on the portfolio value and the sign of the net duration doesn’t change with the magnitude of the shift - yes or no?
Convexity can be positive or negative, so it can act in the opposite direction as duration. Furthermore, as the change in rates increases, the convexity adjustment grows with the square of the rate change, while the duration is only linear. This way, the convexity effect is larger at larger rate changes and perhaps overwhelms the linear effect of duration.
At large rate changes, the convexity effect probably overstates the change in price, but the duration understates it.
The thing is that durations are linear. So a parallel change of x (+10bp) and 20x (+200bp) should have the same sign (and the net change in value should be 20x as large as well). In order to get a sign change, you need some kind of non-linearity that either kicks in or disappears at high values, which is why I was looking at convexity as an explanation.
Unless “overall loss” and “overall gain” refers to assets exceeding the value of liabilities. It could be that the change in value is the same direction, but that the change isn’t actually large enough to eat up all the net equity at x but is by the time it reaches 20x.
Thank you for lots of insight and help with tackling the problem! Normally I don’t work with market risk so your inputs really helped to focus my attention.
I will try to shortly answer the questions that came up:
Duration on-balance: OAD is slightly higher on the asset side - app. 0,7 compared to 0,6 on the liability side. So this speaks rather against a gain from positive interest rate shock.
Duration off-balance: The OADs for the entire off-balance is app.50. None of the derivatives should be speculative but used as hedges. There are predominately payer swaps and a relatively low amount of long interest rate caps.
It seems that the caps eventually cause the described effect by creating convexity in the portfolio, although at first they seemed not very significant to me. However bchad is right when saying that any multiplying effect of the swaps on the duration should have the same sign in case of both +10bp and +200bp shifts. Hence this should not cause the inverted signs.
Thank you anyway for your inputs and an interesting discussion!