# Essays on Investment Math Problem

Outline Problem 16, page 185Problem 29 page 214Problem 20 page 255Problem 20 page 305Proble11, page 343References Appendix – excel files Problem 16, page 185a). The probability on put option of the HPR can be calculated using the following table At this point we should not that the purchase is 100 and the put option is 12. If dividends of the asset are paid during the life of the option the underlying value of the asset is expected to decrease. Put option increases with the payment of dividends while call option decreases with the payments of dividends.

As the time to expiration increase both put option become more valuable. This happens because the longer the time to expiration the more time is available for the underlying asset to move which increases the value of the both put option (Poon and Granger, 2003). b). cost of the index fund and put option The probability distribution of the HPR consisting of one share of the index fund under put option is shown below; The cost of the index fund plus the cost of the put option is 112.c).

When one buys a put option is guaranteed his money regardless the state of the market. Therefore it acts as an insurance of recovering your investment. It is a form of hedging for the investor. It is used to protect a downside of the stock market. The option usually gives the buyer rights to be able to sell underlying asset at a price which is fixed at a time prior to its expiration date which the buyers pays the price for the right. If the strike price is less than underlying asset the option is not exercised and expires worthless; while, the strike price is more than the underlying assets the put option owner exercise the option and sells the stock at the strike price and claims the difference between the asset market value. Problem 29 page 214The client has a degree of risk aversion of A=3.5.

If the investor chooses to invest in a passive portfolio, he will select a proportion that matches his risk perception. It is calculated as follows; Proportion = Proportion == =0.429This means that optimal proportion for the client is: 42.9% invested in the risk portfolio and 57.1% invested in T- bills. b) The fee that one expects to pay or charge a customer for this is equal to the original fees regardless the asset allotted.

Asset mix is irrelevant in the amount of fee charged to client as it depends on amount spend not on the mix. A fee or sales charge is often assessed when a fund is purchased. When this occurs, the fund is referred to as a front-end local fund. When the fee is assessed upon redemption of the shares in a hedge fund, the fund is referred to as a back-end local fund.

Often the exit fee is reduced as the investor’s holding period increases. This encourages the investor to leave the funds under the control of the management company for a longer time. These include investment advisory fees and administrative expenses. Some funds also charge services fees. These fees cover the commission paid to brokers called trail commissions. These fees are assessed annually whereas the black-end and front-end loads are onetime charges.

The investors should carefully consider the nature and extent of fees that the various hedge funds and can significantly impact performance over time. The fees are disclosed in the fund’s prospectus as are many others facts about the funds its investment philosophy and management style (Santa-Clara and Yan, 2006).