Fixed Income Hedge Fund interview prep

Based on interviews I appeared back in the day( before 2019) for fixed income macro and relative value hedge funds in London and information from friends working for some of these, I’ve come up with a list of topics one could prepare if one were interested in a career at these hedge funds. I’ve also explained what each topic involves. I might add to this list in the future if I recollect anything I’ve missed.

Most of the HFs I interacted with aren’t much into exotics (in fact Eisler is the only one) and the questions aren’t that complicated so one doesn’t need to get too quanty about any of the topics I discuss below.

Well first of all, idea to write this post came from viewing a Linkedin ad recently for a fixed income quant in London/NY at Hudson River posted by Antoine Savine, whose work in quantitative finance (automatic differentiation, volatility) I follow. I think it is an amazing opportunity for anyone interested in the job side of things.

Coming back, the following is the list of topics one should be comfortable with (doesn’t have to be an expert in) to have a decent chance of success. One way to look at why these are important is also by how frequently they appear in a typical rates quant library in terms of usage when writing code to price any non-linear product.

1. Yield Curve construction:

   1. Benchmark interest rate instruments used to construct discount factors. First figure out what instruments are needed to construct the mother of all curves, the US dollar curve(s)

   2. Coming from a Libor background (may it rest in peace!) I’m looking at: deposit rates(<3month), FRAs, euro-dollar futures(EDFs), Libor swaps (1y - 50y), tenor basis swaps, FRA-OIS basis, OIS basis swaps, OIS futures, OIS swaps and a few more. For non-US currencies I’m also looking at: cross-currency(xccy) basis swaps(resettable/non-resettable), xccy OIS basis, FX fwd/point. Go through what these instruments are and how you’d price them with focus also on the funding index used. Add in Jumps around Fed rate hike days and turns. Also add in EDF-FRA convexity adjustment as an input. The OIS coupon on the swaps or the future can be based on averaging or compounding the overnight rate. The averaging ones are a little fancier than the others due to a need to compute convexity adjustment for the averaging feature.

   3. Next step is to use the above benchmark instruments to back out via bootstrapping the discount factors on specific dates/times in the future (call them ‘node points’) when these instruments either pay coupons or mature.

   4. Now the fundamental building blocks of a yield curve are instantaneous forward rates, integrals of which are the discount factors (rather log of the discount factors). In order to get discount factors at all times i.e. construct a full yield curve, we try to come up with a formula(polynomials, b-splines etc) for these instantaneous forward rates conditional on knowing their integrals i.e. (log of) discount factors at the node points which we already computed in step ‘c’ above

   5. Having constructed the curve(s) read about how to compute yield curve risk for any given product. Would you bump each benchmark instrument to compute delta point-wise OR a Jacobian approach? For reference go through Vladimir Piterbarg’s Interest Rate modelling book Chapter 6 (Yield curve construction and risk management).

   6. Yield curve construction is a vast topic with much more to discuss, specially on interpolation, and I’ll come up with a separate post on that in the future

2. Rates Vol surface:

   1. In Libor world, there were swaption and caplet vol surfaces (latter much less in use than former). Now there are OIS swaption vol surfaces (ex: SOFR vols).

   2. In all cases, vols are parameterized based on Pat Hagan’s approximation of a displaced SABR model.

   3. Hagan’s approx. of SABR model has issues at low strikes where the modelled distribution can be negative in addition to also leading to unrealistically high vols; there are also issues calibrating to market vols at high strikes. At low strikes this can partly be dealt with using the displacement parameter or patch it with a displaced black model(make sure CDF is smooth while patching). At high strikes, one can have a cut-off strike beyond which vol converges smoothly to the vol at that cut-off strike.

   4. This topic is vast and with heavy math with SABR itself having many variations (exact SABR, modified Hagan, and other SABR like models) so I’d suggest don’t get too deep into it before an interview else you’ll lose track of the bigger picture. I’ll write a separate post on rate vols in the future

3. CMS replication:

   1. Here we are trying to compute convexity adjusted CMS forwards. Think of a simple example of a contract that pays a fixed maturity swap rate (times Notional) at some future date fixed at/around that date. These appear when pricing CMS linked trades like CMS spreads options(steepeners/flateners), CMS spread range accruals. When we price these, one needs to compute convexity adjusted CMS forwards first and foremost and then proceed to do the rest (spread option pricing, digitals etc)

   2. You need an expected value(in the annuity measure) of that swap rate (sometimes multiplied by a discount factor depending on when that swap rate is paid out).

   3. Once you come up with functional forms for both the annuity and discount factor (if any) in terms of the swap rate you can solve the expectation. Roughly speaking, density function→ d2C/dK2(Breeden/Litzenberger)→ shift 2nd derivative from option term to integrand→ weighted average of payer/receiver swaptions i.e. the replication formula. Standard stuff like in VIX derivation. You can refer to the below paper for details: (paper goes via put-call parity to get fwd) https://www.deriscope.com/docs/Hagan_Convexity_Conundrums.pdf

   4. One thing to note, given the replication formula involves pricing multiple swaptions at a range of strikes including wings choosing an appropriate vol surface interpolation scheme is necessary! (topic 2 above)

4. Miscellaneous topics:

   1. Pricing Range accrual digitals: digitals as call spreads

   2. Midcurve swaptions: relation between midcurve, swaption & fwd vol

   3. Convert normal vol → black vol → displaced diffusion vol (given a displacement parameter)

   4. For relative value HFs: try understanding basics of a relative-value bond trade going though initial chapters of the book Treasury Bond Basis by Galen Burghardt. Also maybe go through Salomon Smith Barney’s Principals of Principal components paper for looking at risk.

   5. For the Hudson river job I mentioned at the beginning, the description mentions PnL attribution as well. If we take a Callable CMS spread swap for example i.e. a swap that pays option on a cms spread periodically for receiving a funding rate and that can also be called on those cms spread payout dates, the Pnl attribution exercise will have Pnl from one day to next attributed to the following:

      1. Yield curve risk: risk to Libor, OIS & other benchmarks, both 1st/delta and 2nd/gamma order pnls

      2. Swaption vol risk: to each SABR parameter, both 1st and 2nd order pnls

      3. CMS spread vol risk: to each atm vol, risk-reversal, strangle parameter of the CMS spread vol surface. Both 1st and 2nd order pnls

      4. Model risks (tree model, swap variance/covariance model & any other model risks)

      5. I’ll write a separate post on this in the future on how to calculate each of these components

Although this might look a little too in-depth content wise on each topic, and this is because I was trying to make it a bit exhaustive, one only needs to have an idea about each of the sections. None of the HF interviews I faced were complicated(when compared to a bank). Also, given I’ve no demonstrable experience working on government bonds (treasuries/EGBs/JGBs/KTBs) I was rarely asked questions on bonds even at RV funds.

Happy reading!