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I have a question regarding Bank Discount Yield and Money Market Yield for US TBill.

Some books mentioned that Bank Discount Yield is not a meaningful measure of the return for the TBill because:

  1. The yield is calculated based on face value, not purchase price.
  2. The yield is annualized into 360 days, not 365 days.
  3. The yield is based on simple interest and ignores compouding.

The book also suggests that Money Market Yield is superior to the Bank Discount Yield because it is computed relative to the purchase price, not the face value.

I don't understand this because the equation of calculating Money Market Yield is:

 (360 x R) / (360 - t x R)

where R is the Bank Discount Yield, t is the holding period.

I think the Money Market Yield is solely calculated from Bank Discount Yield. It is not calculated from the actual purchase price.

If Bank Discount Yield cannot be used to measure the return, why the Money Market Yield can?

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The money market yield can be computed directly from the purchase price as $Y_{mm}= \frac{100-P_0}{P_0}\frac{360}{t}$

See for example equation 9.3 here http://www.icmagroup.org/assets/documents/Media/Bondmarketsbook/Bond%20markets_structures%20and%20yield%20calculations.pdf

The calculation of the BDY first and then conversion to MMY with your conversion formula is not necessary. The BDY, as your textbook indicates, is fairly useless in any case. Might as well calculate MMY directly.

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