There are several yield equations in the BOK that you could potentially be tested on when you’re taking the CTP exam. So, I’ll be suggesting some study tips to help you prepare for exam questions where you will be required to recall and solve yield equations. I’d like to begin by putting the yield equations in their “operational context”. That is, answering the questions of “why” and “how” they are used to manage the short-term investment portfolio.

I found, when I was managing the short-term investment portfolio, that on any given day I would be offered a large variety of competing investment opportunities. And if two of these investments had relatively the same amount of low risk and similar maturity dates, then my only decision was to select the one with the highest yield. However, the investment with the highest yield is not always obvious since competing investments can be quoted on either a 360 or a 365 day year and to complicate matters more, can be sold on either an interest bearing or a discount basis. Given this, the annualized yield equations are used to “level the playing field” between two competing investments so that the portfolio manager can make an informed decision as to which investment has the highest yield.

So, I’ve put the yield equations that are covered in Chapter 11 of the BOK in the   following three categories with their suggested study tips.

Annualized Yield Equations: Discount Rate (DR), Money Market Yield (MMY) and Bond Equivalent Yield (BEY)

These three equations can be studied in two steps.

First, you must be able to recall the following equations:

     Dollar Discount           =   Par Value   -   Purchase Price

     Dollar Discount           =   Par Value x DR x Maturity Days / 360

     Discount Rate (DR)     =   $Discount / Par Value   x   360 / Maturity Days

Second, you only need to be able to recall how slight changes, shown in Bold, to the DR equation will give you the MMY and BEY equations, as follows:

  Money Market Yield (MMY)    =   Discount / Purchase Price   x   360 / Maturity Days

                                          Par Value changes to Purchase Price

  Bond Equivalent Yield (BEY)   =   Discount / Purchase Price   x    365 / Maturity Days

                                          Par Value changes to Purchase Price and 360 changes to365                                                                  

Commercial Paper Nominal Yield (CPNY)

GOOD NEWS!!!  You don’t have to learn this additional equation because if you can recall the (BEY) equation by using the “tip” outlined above, you’ve already got it.

    CPNY    =   $ Discount / Purchase Price    x    365 / Maturity Days

Holding Period Yield (HPY)

This equation does not annualize the yield of an investment and as such is not used to  “level the playing field”, as mentioned above, for the purpose of selecting an investment with the highest yield.. However you could get a HPY calculation as an exam question, so here it is simply stated as:

      HPY   =   What you Get   /   What you Pay

For an investment sold on a Discount basis:

      HPY   =   Par Value   -   Purchase Price   /   Purchase Price

For an investment sold on an Interest Bearing basis (i.e. MMY  basis):

       HPY   =   Interest Earned   /   Par Value

                 Where:  Interest Earned   =   Cash Received at Maturity   -   Par Value

-          George Schilling, CTP