Historical Vs. Implied Volatility

Choose two stocks from the same industry to minimize the influence of other confounding factors. You choose the industry that you are relatively more familiar with, and then estimate the implied volatility and historical volatility of the two stocks. The former is estimated based on their option values (refer to Ch. 13 for implied volatility). For convenience and especially if you are using my program, choose stocks with zero or low dividend yield (please specify the dividend yield in your report). Information needed here can be obtained from major financial websites such Yahoo Finance, but you can also use our Bloomberg terminal.

Answer the following questions, and the discussion of each is limited to one page each question.

1) Briefly discuss the two firms of your choice, and in the discussion, must include risk analysis and financial ratios (especially those related to risk). Which firm seems riskier?

2) Estimate the historical standard deviation for the two stocks: You need to obtain historical stock prices, either from Bloomberg or Yahoo Finance. Stock prices need to be transformed into returns. For example, You can calculate the logarithmic return ln(s_t/s_t-1) or the arithmetic return = (stock price on day T - stock price on day T-1)/ stock price on day T-1.A minimum of 30 returns is required. The standard deviation (SD) of Stock Returns can then be estimated using EXCEL function STDEV(range of return data) or the following formula:

.Convert the SD to annual standard deviation; if you use daily returns, the SD you obtain is a Daily one; you need to transform it to Annual SD = Daily SD * (252) ^0.5 Describe how you got the answer. Which stock has higher historical volatility and does it make sense?

3) Implied volatility: For each of the stocks, find the market values of three call options on the stock (from sources such as Yahoo Finance): One should be near the money, and the other twoin and out of the moneyuse options with considerable trading volume; the reason is that if an option is not heavily traded, its market price might not adequately reflect its true value or the market price is simply a stale price. You should also avoid options with just a few days to expiration, since the value of these options do not strongly depend on volatility. Use either the text's software or my program to compute the implied volatility (be sure to enable Macro if you are using my program). Show me how you get the answer by including your inputs (S, K, r, T) and specifying the program you are using. Bloomberg terminal actually computes implied volatility too, but because we can't see the program, you are not allowed to use Bloomberg for the purpose of estimating implied volatility. Which stock has higher implied volatility and does it make sense?

4) Overall conclusion