In response to my piece on “this may be a great time to buy bonds”, one of my readers sent me a personal mail asking to understand the difference between clean and dirty price when it comes to bond investing. Like I often do, when I receive emails on something I think demands public or general consumption, I prefer to respond with articles rather than an email to a single reader so that all my beloved readers can benefit from the question asked. That is the reason for this article.

In stock investing, when companies declare dividends, they set up a date to close the books. The implication of this process is that if your name is not in the company register as at the date of book closure you will not receive the dividend. From that date, the shares of the company are marked ex div, meaning without the dividend. Prior to that date, the shares are marked cum div, meaning cumulative or with dividend. This implies that anyone buying the share during the cum div period will pay two prices, the regular price of the share and the dividend amount because as at the record date when the book closes, the seller’s name would have been expunged from the register. In order not to lose the dividend declared before the sale but payable after the sale, the buyer has to buy the shares at the cum div price.

That principle applies to bonds also but bonds do not pay dividends rather they pay interests. Unlike dividends that depend on the decisions of the board of directors of a company, interest payments are contractual and obligatory. In that case, one knows how much interest one is required to receive from a particular bond at each interest payment date. However, for proper accounting, the interests are accrued on a daily basis until payment date. Not everyone holds a bond till maturity and not everyone holds a bond till the interest payment date. When bonds are sold between coupon dates, the seller needs to be compensated for the accrued interest for the period he held the bond. This is where the issue of clean and dirty price comes into play.

Source: Quantitative Financial Analytics

A bonds clean price is the price of a bond without accrued interest. It is to bonds what ex-date price is to stocks. On the other hand, the dirty price of a bond is the clean price of a bond plus accrued interest. It is to bonds what cum div price is to stocks. If you are lucky to buy a bond on the interest payment date, you will be faced with just one price because the clean and dirty prices are the same because all accrued interest have been paid. It may not be apparent if the quoted prices are clean or dirty, so you need to find out from your broker or bank but if you know the yield to maturity of a bond and you are mathematically inclined, you can easily apply discounted cashflow analysis for the valuation of any bond using the formula to figure out the price.

The above formula calculates the clean price of a bond, so, if your calculated price matches the quoted price, at least, approximately, then the quoted price is clean. Note that in the above formula, C represents coupon payment, F represents the face value of the bond, t is time to maturity while r is the yield to maturity. Even if you are not mathematically inclined, bonds can be easily valued with excel spreadsheets using the formula PRICE(settlement, maturity, rate, Yld, redemption, frequency) where settlement is the day your bond trade settles, maturity is the maturity date of the bond, rate is the coupon payment, yld is yield to maturity of the bond, redemption is the face value and frequency is how often the bond pays interest in a year, 1 for annual, 2 for semiannual and 4 for quarterly pay.

How are Bond Prices Quoted in Nigeria?

Analysis by Quantitative Financial Analytics Ltd indicates that most Nigerian bonds quoted on FMDQ website are priced or quoted clean as the table above shows.

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