Small firm effects put forward by arbel and stebel

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Unformatted text preview: return. T HE PUT-CALL PARITY THEOREM The put call parity theorem suggests that following no arbitrage equilibrium pricing relationship, the value of a European put option with the same exercise price and expiration date as the above European call option is defined as: P = C + Xe-rt – S T HE PUT-CALL PARITY THEOREM PROOF 17 Cheryl Mew FINS2624 – Portfolio Management Semester 1, 2011 P ROFITABLE RISK FREE ARBITRAGE OPPORTUNITIES If the current value of 1 portfolio is greater than the other, investors may sell the more expensive portfolio, invest in the cheaper portfolio and have surplus cash to spend or invest at the risk free rate. There is no risk to this strategy, because on maturity date, the values of the 2 portfolios will always offset each other. The following illustrates how the process works: On maturity date, no further inflow/outflow will occur irrespective of the stock value. Thus the profit made today is risk free and is known as an arbitrage profit. In a perfect market with no transaction costs, traders are expected the correct the mispricing as soon as it arises and eliminate the arbitrage opportunity so that (C+Xe-rt) = P+S. U NDERSTANDING THE COMPONENTS OF THE BSOPM A NNUALIZED CONTINUOUSLY COMPOUNDED RETURN ON A RISK FREE ASSET Bank bills are commonly considered as risk free assets as: 1. 2. 3. The issuing bank guarantees their performance Bank bills do not pay any coupons and investors receive the face value at maturity Bank bills are classified as a discount security and investors are not exposed to any income or price risks if they hold the bank bills to maturity. r, is the rate in which the bank bill will be discounted at. T IME TO EXPIRATION IN YEARS (T) The time to expiration in years is found by dividing the number of days by 365. 18 Cheryl Mew FINS2624 – Portfolio Management Semester 1, 2011 A NNUALIZED SD OF CONTINUOUSLY COMPOUNDED STOCK RETURNS σ measures the volatility of the underlying stock over the remaining life of an option. As this variable is not observable, it is a common practice to use the historical standard deviation of stock retur...
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