HELP > Bond	Back \| Print

select a topic:

<< Back | Next >>

PRICE

A bond can be regarded as a flow of capital (coupons and principal) that will be paid out in the future at dates specified in the prospectus. However, in order to determine the present value of a future payment, it is necessary to update taking into account the loss of purchasing power due to inflation. To calculate the price of a bond, one simply has to update each payment and add up the figures. To do this, a simple approach is to admit that there is only one identical rate for all maturity dates (the rate curve is flat) .

The following formula allows us to make this calculation:

Cpn: Amount of paid coupon
Rbt: Redemption value
YTM: Yield to maturity
Freq: Number of coupons paid per year
N: Total number of coupons to be received
a: Fraction of year covered by the accrued coupon

This formula serves to calculate what is known as the ‘dirty price’, the price that includes accrued interest. However, by convention, bonds are treated at their ‘clean price’, that is, the price not including accrued interest.

Dirty Price = Clean Price + Accrued Interest
Clean Price = Dirty Price - Accrued Interest

The greatest weakness of this method of evaluation is the use of a single rate to update a payment flow with distinct maturity dates, which is inconsistent with the actual situation because the rates are different depending on the maturity. Moreover, one does not know which rate to use (the one-year rate, the five-year rate, or others). To provide a more accurate figure, each flow should be updated according to the rate that is appropriate for its own timing. This latter method of evaluation is an approach that is theoretically correct, but that assumes that the structure of the rates is accurately known. Besides, even if the rate structure were perfectly well known, the general evaluation principle only allows classic bonds to be evaluated .

BID PRICE

The bid price is the bond’s evaluation price from the seller’s side. It is the net percentage price that will be paid to the investor who wishes to sell a bond .

The total amount received by the seller will be: (Par Value) x (Bid Percentage) + Accrued Interest

Example :
How much would you receive by selling €100,000 of the issue shown below at the value date of 11.11.2005?

Par Value = 100'000 x 119.02% = €119'020
Accrued Interest = €3'123
Montant total = 119'810 + 3'123 = €122'143

ASK PRICE

The ask price is the bond’s evaluation price from the buyer’s side. It is the net percentage price that will be paid by the investor who wishes to buy a bond .

The total amount to be paid by the buyer will be : (Par Value) x (Ask Percentage) + Accrued Interest

Example :
How much would you pay for €100,000 of the issue shown below at the value date of 11.11.2005?

Par Value = 100'000 x 119.17% = €119'170
Accrued Interest = €3'123
Total = 119'170 + 3'123 = €122'293

BID-ASK SPREAD

The bid-ask spread is the difference between the sale price and the purchase price of an issue.

The bid-ask spread represents the margin of the ‘market maker’. Indeed, the market maker buys a debt instrument from an investor at the bid price, and sells it to another investor at the ask price.

This measurement is a good indicator of the issue’s liquidity. The lower the quality of the issue, the higher the bid-ask spread set by the market maker to cover its risk.

<< Back | Next >>