XD adjustments

I'm a bit confused about dealing with situations in which you are presented with XD adjustment and income (and also, to make things particularly jolly, tax).

For example assignment X4 Question 9 part (iv) gives;

• a series of capital values I(t);

• a series of XD adjustments XD(t);

• a series of accrued interest amounts Acc(t).

It asks you to calculate a suitable total return against which to measure a fund over a three month period, assuming the fund pays 30% tax on income (only).

The solution gives the following formula for the total return from one period to the next;

TR(t-1,t) = {I(t) +(1-T) [XD(t)-XD(t-1)]-T(Acc(t)-Acc(t-1))}/I(t-1)
​

Right, I get the bit about stripping out the tax on the XD series at the rate at which the fund is paying tax. However, it's the accrued interest bit that baffles me. I thought the XD adjustment itself was supposed to represent income (in this case coupon payments) over the year to date. In that case, what's the second adjustment about? Is it interest on the income?

Please let me know if anyone has any thoughts on this.

Thanks

Irn Bru

 

See the ActEd comments on this in chapter 14.

I think the point is that when you actually receive a coupon you pay tax (reflected in the xd adjustment bit), but also between coupons you the bond is accruing interest, so you should also pay tax on the accrued interest to date (maybe think of this as a "earned" amount from an accounting perspective).

I think tax on the accrued interest bit would only really apply if you sold the bond prior to the next coupon date (as a proxy for capital gains, but via income tax?).

Probably the notes need to be expanded on this topic.

 

Consider the following example to illustrate the interaction between the ex-dividend adjustment and the accrued interest.

Suppose a bond is priced at I(1)= 101 on 1st Feb and I(2)=103 on 1st Oct. These prices are dirty prices, ie including accrued interest, as are the prices used in bond indices (see Chapter 14 page 20).

Suppose also that a twice-yearly coupon of 6 is payable on each 1st July and 1st Jan.

Then. if the xd adjustment is 6 on 1st Feb, it will be 12 on 1st Oct, the increase reflecting the coupon paid on 1st July.

Also, the accrued interest on 1st Feb will be 1 (since it is 1 month since the last coupon was paid on 1st Jan), whereas on 1st Oct it will be 2 (since it is 1 month since the last coupon was paid on 1st July).

The total net of 30% income tax return will therefore be:

[103 - 101 + (1 - 0.30)(12 - 6) - 0.3(2 - 1)]/101 = 5.84%

As it says near the top of page 15 in Chapter 14, the tax on the accrued interest needs to be deducted, as accrued interest is incloded in the dirty prices, with which the index is calculated.

 

Can you clarify if this is purely for accounting purposes - I.e. If you sold the bond prior to the next dividend that extra bit of tax on accrued interest would end up getting paid as a capital gain, not as income.


So this must be on an accounting basis under the assumption you will not sell?

 

I'm pretty sure that accrued interest is counted as income for tax purposes - hence it's inclusion in the net of tax return formula in the Core Reading.

Accrued interest is important primarily for tax calculations. In the UK, pension funds are not taxed on bond returns, whereas most investors are. So, what used to happen is that other investors would sell the bonds to pension funds immediately before they went ex-dividend (as the coupon was worth more to the gross pension fund than to the net investor) and then buy them back afterwards.

So, the rules were changed so that investors pay income tax on accrued interest (even if they never actually received any coupons.)