The Markowitz Frontier in this economy

Assume that it is now 1 April 2019. Javid plc has identified the need to invest £15 million for a six-month period from 1 June 2019. The current spot interest rate is 4.5% p.a., and the finance director of Javid plc wants to protect the company from interest rate falling below 4% p.a. and is considering the use of traded interest rate options on 3-month sterling futures. Information regarding these options on futures (standard size £500,000) on 1 April 2019 is as follows (premiums in annual % terms):
Calls Puts
Strike price June September December June September December
95.50 0.19 0.23 0.26 0.16 0.73 1.54
95.75 0.11 0.13 0.17 0.29 1.13 1.95
96.00 0.08 0.10 0.14 0.49 1.37 2.21

Calculate the effective annual interest rate achieved if, on 1 June 2019:

(i) The spot rate is 2.72% p.a. and the futures price is 97.55
(ii) The spot rate is 5.34% p.a. and the futures price is 94.46

(b) A two-asset economy comprises assets with the following parameters:
Asset 1 Asset 2
Expected returns (p.a.) 24% 14%
Variance of returns 25% 4%

The covariance of returns between the two assets is 0.04.

Find the Markowitz Frontier in this economy.

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