The following yleld data relates to a number of high-quality corporate bonds recorded at each of the three polnts in time: Today Maturlty years) 1 5 years ago 9

5 Years Ago:

YTM of 5 Years Bond = 9.37%

YTM of 10 Years Bond = 9.55%

Since nothing is given, it is assumed that the interest rates or YTM given above are for p.a. annually compounded as is the general case.

Now,

As per Expectations theory, we can find out expected future short term YTM or interest rates based on longer term rates today. So, for finding out the future 5 years YTM 5 years ago, investor can use long term i.e. 5 Years and 10 Years bond YTM. Below formula is used for the calculation:

Expected 5 Year YTM = ((1 + YTM of 10 Year Bonds)¹⁰ / (1 + YTM of 5 Year Bonds)⁵)^{(1 / 5)} - 1

Expected 5 Year YTM = ((1 + 9.55%)¹⁰ / (1 + 9.37%)⁵) ^{(1 / 5)} - 1

Expected 5 Year YTM = (1.5909)^{(1 / 5)} - 1 = 9.73%

Thus, investors would have expected 5 year YTM of 9.73% as of today 5 years ago. This is what they could have locked in by trading these 2 bonds.