Question

And investor in treasury securities expects inflation to be 2.3% in year one 3.1% in year two and 4.2% each year there after assume that the real risk free rate is 2.45% and that this right when we remain constant three year treasury securities yield 6.10% wow five year treasury securities you'll 7.60% what is the difference in the maturity risk premiums on the two securities that is what is MRP five minus MRP three

Answer 1

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Given:

Risk free rate = r^* = 2.45%

3 year treasury security yield = T₃ = 6.10%

5 year treasury security yield = T₅ = 7.60%

Rate of inflation = 2.3% in year 1, 3.1% in year two, 4.2 each year there after

Calculation of inflation premium

IP₃ = 2.3% + 3.1%+ 4.2% / 3 = 3.2%

IP₅ = 2.3% + 3.1% + (4,2% * 3) / 5

= 2.3% + 3.1% + 12.6% / 5

= 3.6%

Formula : T_t = r^* + IP_t + MRP_t

Calculating MRP₃

T₃ = r^* + IP₃ + MRP₃

  6.10% = 2.45% + 3.2% + MRP₃

6.10% = 5.65% + MRP₃

   MRP₃ = 6.10% – 5.65%

MRP₃ = 0.45%

Calculating MRP₅

T₅ = r^* + IP₅ + MRP₅

7.60% = 2.45% + 3.6% + MRP₅

7.60% = 6.05% + MRP₅

MRP₅ = 7.60% – 6.05%

MRP₅ = 1.55%

So, MRP₅ – MRP₃ = 1.55% – 0.45%

= 1.10%

MRP₅ – MRP₃ is 1.10%