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 = T_{3} = 6.10%

5 year treasury security yield = T_{5} = 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

IP_{3} = 2.3% + 3.1%+ 4.2% / 3 = 3.2%

IP_{5} = 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 MRP_{3}

T_{3} = r^{*} + IP_{3} +
MRP_{3}

_{ }6.10% = 2.45% + 3.2% +
MRP_{3}

6.10% = 5.65% + MRP_{3}

_{ } MRP_{3} = 6.10% – 5.65%

MRP_{3} = 0.45%

Calculating MRP_{5}

T_{5} = r^{*} + IP_{5} +
MRP_{5}

7.60% = 2.45% + 3.6% + MRP_{5}

7.60% = 6.05% + MRP_{5}

MRP_{5} = 7.60% – 6.05%

MRP_{5} = 1.55%

So, MRP_{5} – MRP_{3} = 1.55% – 0.45%

= 1.10%

MRP_{5} – MRP_{3} is 1.10%

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