When to use PV or FV in the calculation of Bond Equivalent Yield.

CFA Level I Fixed Income
#1

Hi,

i am very confused when to use:

  1. the calculation for PV or FV and

  2. PV or FV in the denominator for the calculation of the bond equivalent yield.

From the question below, it seems that the use of PV and its use as a denominator applies when a Discount Rate is given and FV should be used when an Add-On Rate is given. If my understanding is correct, why so?

Appreciate your help on this please.

Thanks and have a good weekend!

Suppose that a money market investor observes quoted rates on the following four 180-day money market instruments:

Money Market Instrument Quotation Basis Assumed No. of Days in the Year Quoted Rate

A Discount Rate 360 4.33%

B Discount Rate 365 4.36%

C Add-On Rate 360 4.35%

D Add-On Rate 365 4.45%

Calculate the bond equivalent yield for each instrument. Which instrument offers the investor the highest rate of return if the credit risk is the same?

Solution:

A PV=100 x [1 - 180/360 x 0.0433] = 97.835

AOR= [365/180] x [(100-97.835) / 97.835] = 0.04487

The bond equivalent yield for Bond A is 4.487%

C FV=100 + [100 x (180/360) x 0.0435] = 102.175

AOR= [365/180] x [(102.175-100) / 100] = 0.04410

The bond equivalent yield for Bond A is 4.410%

#2

Hi, just realised that i’m still not quite sure about this.

Can anyone advise?

Thanks!

#3

The way to think about this is that you need to compare apple to apple:

1- you need to convert the discount rate to add-on rate

2- change from 360 to 365 days. “remember Bond Equivalent yield is based on 365days”

once you have a uniform quote across all money market rates, only then you can compare.

the starting point is to understand the difference between discount quotation or add-on quotation:

Discount quote: say a bond is quoted on a discount basis of 5% this means that Discount value/FACE value -1 = 5%. it’s like saying (100$ - 95$)/100$.

Add-on quote: 5% is over and above the face value so it looks like this: (105$ - 100$)/100$ = 5%

Now let’s convert a discount rate into an add-on rate using the same example:

the add-on equivalent rate for the discount quote would be (100$ - 95$)/95$ = 5.26%

Beware that you need to adjust for the quoted period, like in your example for 180 days. so let’s look at

instrument A:

1 - Discount rate is 180/360 x 4.33% = 2.165% so discount value is 97.835$.

2 - Convert to add-on (100$ - 97.835$)/97.835 = 2.213%

3- Annualize your add-on rate based on 365days 2.213% x (365/180) = 4.487%

So now you have 4.487% add-on rate based on 365 days.

Instrument B:

1- Discount rate is 180/ 365 x 4.36% = 2.15% so discount value is 97.85$ ( Beware this is already based on 365days).

2- Convert to add-on (100-97.85)/97.85 = 2.197%

3- Annualize it back to 365. 2.197% x ( 365 /180) = 4.455%

So now you have 4.455% add-on rate based on 365 days.

Instrument C:

is already an add-on rate. you just need to adjust it to 365days

1- 4.35% x (180/ 360 ) = 2.175%

2- 2.175% x ( 365 /180) = 4.410%

And you have 4.410% add-on rate based on 365days

Instrument D is already an add-on and based on 365days, so now you can compare all 4 instruments.

#4

wow, thanks Nicholas for taking the time and effort to write such a detailed explanation.

I get it now. Very much appreciated! yes

#5

my pleasure