期權期貨題目 求解

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a local bank offers you a deposit instrument that guarantees that investors will receive a return during next six-month period that is the greator of (a)zero (b) 40% of the return provided by the Hang Seng Index. Assume that the risk free rate of the interest is 8% per annum, the dividenf yield on the index is 3% per annum, and the volatility of the index is 25% per annum. Is the product a good deal for u?

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关键词：Instrument Guarantees Volatility Investors Guarantee instrument receive interest provided deposit

印象中, 這好像是 John Hull 那本書 "Greek Letters" 章節內 Further Questions 的題目, 要是沒人回的話, 可在論壇找看看解答 獲我有空再回

I think the question can be rewritten as which choice below has higher value?

1) Expected value of option after 6 months
2) Risk free return after 6 months

the cost is approx  4%.
but the option is worth only 6.8%, among which
0.5 * ( 8% - 3%) * 0.5 ~1.2% is dividend adjustment, and 5.6% is from vol.
multiply by 0.4 ~ 2.8% < 4%.
so not good deal.
needs ~ 60% of return to breakeven.