Archive for the ‘Trading’ Category

Bond ladders

May 3, 2012

Never heard of bond ladders?

Well neither had I until a few months back. I was running some tests on a sample bond portfolio and discovered a seeming paradox:

A portfolio that is long bonds may actually benefit from a sell off!

The explanation is that you benefit when you reinvest the coupons that your portfolio pays: the bonds you buy are cheaper.

This is a problem of reinvestment risk, and the concept of a bond ladder should be better known as a standard building block for a bond portfolio – it is one way to reduce reinvestment risk.

Here are some articles that give more details: here and here.

Here is an abstract of a more academic pay-per-view paper which discusses bond ladders as a nearly optimal investment strategy.

Smile, it’s Volga!

April 9, 2012

Armed with the Hardy Decomposition for option prices, it now becomes much easier to understand why the smile exists.

To be clear, options trader might use the smile to manage supply & demand, but here we discuss the mathematical basis for smile – which is important if you want to understand how to generate smile in a monte-carlo model.


The current crisis in historical perspective

March 28, 2012

This short post is primarily to give links to three excellent articles on macro economics by Ray Dalio, founder of Bridgewater.

The first, a ‘template for understanding’ how economies work, is better than anything I have ever seen in introductory books on economics.

The other two articles take a closer look at the dynamics of debt and deleveraging, and give a good sense of the processes that we are currently seeing in action at the moment.

Click here to go to the articles.

Fixed-income investment strategies in the age of the New Normal

March 27, 2012

I came across an interesting presentation given by one of the senior members of PIMCO UK, a chap called Mike Amey.

Click here to see it (a PDF).

What I especially like about this presentation is that it covers a lot of the main topics that I hear investors discussing at the moment, ranging from the bigger themes like EMs vs developed markets or the general Health of Economies, global inflation, tail risk, through to the more technical strategies like carry.

In this post I give background and thoughts on some of the topics and terms that Mr Amey uses in his presentation.


A quant trading model for swap spreads

February 7, 2012

I recently wrote quite a long post on swap spreads (click here to see that post), covering some general intuition about swap spreads: what does a swap spread represent, why does it move, when does it move, which direction does it go, etc.

My blog stats show that a lot of people have read it, so it seems that it has been quite useful.

Browsing through quant.stackexchange I found my way to a very interesting article written by Paul Tooter which builds a trading model for 10-year swap spreads. Paul calls himself a quant developer and has written a book and plenty of articles on R, a programming language designed for statistical analysis.

The model uses a linear regression of the 10-year swap spread onto:

  • 10-year treasuries
  • 5-year treasuries
  • 5-year swap rates
  • S&P 500
  • USD Bank stocks

The model is effectively using the 5-year swap spread as part of the signal generation for the 10-year spread. The use of LIBOR, S&P and Bank stocks are not surprising if you have read my post: they are indicators of activities which can move swap spreads.

The buy/sell signal is generated from the residuals combined with a momentum indicator on the residuals.

It’s a great read. Click here to read Paul’s article, and click here to go to his website.

Two top tips for pricing

February 4, 2012

One of the most basic elements of any job on the trading floor is pricing.

This post gives you two important tips that can help you to:

  • reduce the probability of making a pricing mistake,
  • talk to your trader in clearer terms,
  • check that your pricing is reasonable,
  • and generally get a better intuition for what current maket prices mean.

Neither tip is rocket science (by a long way!), but they can definitely spark a Eureka! moment, so they are worth passing on I reckon.


Why does the yield curve slope upwards?

January 26, 2012

In this post I give a short, but I think rather usefully direct reason for why the yield curve should slope upwards. All it requires is for you to put yourself in the shoes of an investor that has to lock up their money in a bond for a fixed amount of time (and a very simple piece of algebra).

Yes, you can find plenty of papers which give complicated economic reasons for why this should be the case, but I tend to think that it is the simple insights that explain most of what you see happening in financial markets.


Everything you wanted to know about Repo but were afraid to ask

January 11, 2012

Well the title is a bit of an overstatement!

This post is actually just a short note with a link to a document which covers the concept of specialness in the repo market, and which is actually a good description of the repo market as a whole. Such things are hard to find, you know.

Click here for the doc.

How to calculate carry

January 11, 2012

Positive carry can be an obsession for fixed-income investors.

For a simple explanation of carry for a bond position have a look at this well-written post: click here.

Facts, rules of thumb, and intuition for swap spreads

January 11, 2012

The N-year swap spread is defined as:

N-yr swap spread := N-yr swap rate – N-yr government bond yield.

Since most quants spend much less time on the bond market than on the swaps market,  they often don’t come to appreciate the central importance of the swap spread. Here is an unordered list of why the swap spread is important:

  • it is the unhedgeable part left over after you hedge a bond portfolio with swaps,
  • it is a value measure of whether investors should buy their exposure with swaps or bonds,
  • it makes up one of the standard collection of arbitrage strategies in the fixed income space,
  • it moves a lot (sometimes up, sometimes down) in times of market stress.

The swap spread is fascinating, believe it.

This post collects a few of my personal notes on the swap spread, including my tricks for remembering the rules-of-thumb, and gives links to well-written articles across the web.