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Yield curves and modified duration – CII exams R02, J10, J12 and AF4

9 May 2019

Analysing the features of bonds is important for anyone thinking of making an investment in this asset class. It is equally important for students of the investment-focused CII exams.  Questions often come up in R02, J10, J12 and AF4.

This post was originally published on the Brand Financial Training Blog at https://brandft.co.uk/yield-curves-and-modified-duration/

and has been reproduced here with their permission. It is relevant to examinable tax year 2018/2019. All content © Brand Financial Training.

In R02 (Investment principles and risk), a candidate will most likely be asked to calculate running yields and/or redemption yields – perhaps both!

In J10 (Discretionary investment management) and J12 (Securities advice and dealing), the question is likely to be more technical, so might ask for the effects of inflation and/or interest rates on yield curves.

In AF4 (Investment planning), it could be any of these things, but with this being an advanced written paper rather than a multiple-choice paper where the answer is there somewhere, this means a greater level of understanding is needed.

In this article, we look at yield curves and modified duration.

Yield Curves

Yield curves plot the interest rates available on bonds against their maturity dates – either those offered by the government or companies.

To draw a yield curve, plot the number of years along the x-axis and the bond redemption yields on the y-axis, then put a dot for as many bonds as you can find and join them together. The shape of the curve can be different at any given time; if the normal yield curve changes, this is an indication that investors need to be looking more closely at what’s happening in the economy.

A yield curve generally slopes upwards from left to right; this is because longer-dated bonds usually have higher interest rates as demanded by the investor for the risks they’re exposed to over a longer period of time and shorter-dated bonds offer the lowest returns to reflect the fact that the investor’s money is at less risk. This is known as a ‘normal’ yield curve.   A normal yield curve shows that investors expect the economy to grow at a ‘normal’ rate.

The important yield curve to watch is those for gilts, as these set the interest rates on mortgages and bank loans.

Occasionally, you might get an ‘inverted’ yield curve. This is when shorter-term yields are higher than the longer-term yields, which can be an indication that the market is expecting longer-term interest rates to be lower, which can often be associated with recession.   Inverted curves are rare, but they should not be ignored by investors.

A flat yield curve indicates stability in terms of inflation and interest rates.

Yield curves give us an idea of what to expect from investments and borrowings over various different timescales and look at the slope of the curve too; the greater the slope, the greater the gap between short- and long-term rates.

Modified Duration

You will already know that one of the biggest risks of holding bonds as an investment is that interest rate changes can have a significant impact on their value; this is known as market or price risk.

There’s an inverse relationship with bond prices and interest rates; as interest rates fall, bond prices go up and when interest rates go up bond prices fall.  The concept of duration allows us to gauge how much a bond’s price is likely to rise or fall when these changes happen.

Duration measures how long it takes in years for the price of the bond to be repaid by its cash flows. Let’s say this has been calculated as 3.41 years.  We can use this figure and the gross redemption yield to then calculate its modified duration.  If we assume the gross redemption yield is 4% – we calculate modified duration as:

Duration of 3.41 divided by (1 + the gross redemption yield of 0.04) = 3.28.

We now know this bond has a modified duration of 3.28 and so can be expected to undergo a 3.28% movement in price for each 1% movement in interest rates.

If the bond had a current price of £108.28 and interest rates rise by 1%, then we can expect the bond price to fall to:

£108.28 – (£108.28 x 0.0328) = £104.73

The longer the modified duration is (in years), the more sensitive a bond is to changes in its yield.

Understanding these particular features of bonds will really help anyone studying for a CII investment exam.

If you’re studying for CII AF4 exam, and you don’t think you’ve had enough practice yet, Brand Financial Training offers a free taster to check out their resources for yourself.