Investing for the Duration

Duration is an important concept in the world of Bonds. It measures the sensitivity of a bond to changes in interest rates. Thus, a bond (or a portfolio of bonds) that has a duration of 5 will be expected to move 5% in price for a change of 1% in the discount rate (i.e .the market rate of interest) [1]. A bond/portfolio with a duration of 10 would see a 10% rise/fall in price for a given 1% move in rates etc,etc. Ceteris Paribus, the longer the maturity, and the lower the coupon, the longer the duration of a bond – think of it in terms of how long it takes to get your money back; the lower the coupon payment on a bond, the longer an investor must wait before his/her investment is fully returned.

What is less widely understood is that equities have a duration too. This is defined as the percentage change in its price for a given 1% change in the long term return that the stock/Index is priced to deliver. It can be approximated by the Price to Dividend Ratio (so, a yield of 4% equates to a Duration of 25 years – 100/4 – a yield of 3% = 33.33 years and so on).

Thus, an investor with no particular view on market direction, and wishing to have the most predictable future portfolio value at some specific future date should aim to have a portfolio duration that matches their investment horizon. This eliminates the risk of fluctuations in interest rates causing an unwelcome drop in asset prices just as one is about to retire for example. To see this, consider that a 20 year (zero coupon) bond will deliver exactly the same value in 20 years time, regardless of where rates move in the interim. (The same applies to coupon bonds as one can re-invest the income periodically so that final wealth is maintained).

This thinking of course, does not apply to Active Managers – they believe that they can vary their portfolio allocations to take advantage of price changes. But they still have an implied portfolio duration, whether they know it or not. Sometimes this gives us a window into fund manager’s attitude to risk, as high stock valuations imply higher duration; contrariwise, the lower the Bond markets valuation (or the higher the yield to maturity), the shorter the overall portfolio duration[2]. So there is a world of difference between a 60:40 stock/bond portfolio when assets are cheap and when they are expensive (on a P/E or on a yield to maturity basis). It appears that their thinking on this issue has not altered at all in response to circumstantial changes…

A typical stockbroker asset allocation might be set at 60% equity, 40% bonds. At an equity market yield of 5% (i.e a duration of 20) and a Bond market duration of 10 years (as pertained post 2008), the overall portfolio duration would be: 0.6 x 20 + 0.4 x 10 = 12=4= 16 years. But the situation changes dramatically if yields on assets generally decline. Currently, the MSCI World Index (a global equity proxy) yields 2.63%, which translates into a duration of 38, whilst the Barclays Global Aggregate Bond Index has a duration of 6.9 years, which means an overall portfolio duration of 0.6 x 38 + 0.4 x 6.9= 23+ 2.7= 26 years. For investors focusing on US Indices, the situation is even more extreme – the S&P 500 for example has a yield of 2.17% which equates to a Duration of 46.1 years. As of November 2014, the yield was just 1.91% implying a duration of 52.4 years – a 100% S&P 500 portfolio bought then would therefore only provide a predictable retirement value to those in their first year at University…

[As an aside, Pension Funds/Life Companies are struggling with their own asset/liability mismatch, due to longevity-related demographic changes – their solution, to buy very long dated inflation-linked bonds is an attempt to address this, but at current yield levels this appears to be exchanging one risk-longevity for another- price volatility. At current levels of yield, tiny changes in Inflation expectations cna have outsize effects on prices. If you further factor in liquidity issues (who are these funds going to sell losing positions to ?), there is potential for trouble].

This has implications for investors “of a certain age”. It is important to consider Portfolio Duration as part of the risk control process – it may be that investors are taking on more risk than they realise. The greater the difference between the Investors’ time horizon and their Portfolio duration , the greater the dependency that they have on the path that stock values (and thus prices) take up to the point of retirement. If an investor has enough to live off comfortably, why should they take the risk inherent in being overly invested in long duration assets ?

[1] To see this, consider a 5 year Zero Coupon bond (the calculations are basically the same for coupon bearing bonds , but it is slightly more complicated to calculate)

With a current discount rate of 2% (for example), the price of a bond maturing at par (£100) in 5 years time will be 100/1.02^5= 90.57.

Suppose that the interest rate rises to 3%, the price will now be 100/1.03^5= 86.26.

If rates fall to 1% , the bond would be priced at 100/1/01^5= 95.15.

(Notice that the percentage decline in price is smaller than the percentage rise in the two situations. This is called Convexity, which gives us two concepts for the price of one. We shall cover this in more detail at a later date).

[2] Next week we shall look at the implications of this from a portfolio perspective, comparing and contrasting some typical fund allocations and that of EBI Vantage/Varius funds.