Financial Analytics

 

Assume a 2 step tree to value a European option that is due in 4 months when the futures price is 85, strike price is 80, risk-free rate is 1.5% and 𝜎 = 0.30.
Draw out the binomial tree to include the futures price at every node and the call/put option values at the ending node.
Compute the initial premiums for a call and a put option. (Show your work)
Repeat the binomial tree (as done in part (a-b)) for an American put and call option.Do any of the premium values change? If so, which one(s)?
Compute the initial premium for the American options.
Download historical futures data for crude oil from quandl using the following command Quandl(“CHRIS/CME_CL1”).
Compute the historical volatility for the month of January 2021.
Compute the monthly historical volatility for each month going back to 1985. Plothistorical volatility by month.
Does the monthly volatility associated with oil appear to be stationary? Conduct anynecessary tests and report your results.
A 1-year option is offered with current stock price of $100. The strike price of the option is $90 and the annual volatility rate is 40%. The risk-free rate of return on a 12-month bond is 2%. When the Black-Scholes model is used:
What is the value of 𝑑1?
What is the value of 𝑑2?
What is the price of a call option, c?
What is the price of a put option, p?

 

Sample Solution

But advocates of SRI claim that it makes more sense to follow sustainable investment strategy to generate superior returns. They list out several advantages which socially responsible firms have over the other firms which make them financially stronger and more profitable.  Socially responsible firms are less likely to face environmental fines; they are less likely to face costly settlements resulting from liability lawsuits for bad quality products; good corporate citizenship may result in increased product sales; and employee loyalty resulting from good employee relationship will help improve productivity, innovation and thus profitability. [2]

Alexander Kempf and Peer Osthoff in their paper “The Effect of Socially Responsible Investing On Portfolio Performance” [1] used SRI ratings of KLD Research and Analytics to form two stock portfolios, one with stocks having high SRI ratings and the other with low SRI ratings. They studied the performance of these portfolios from 1992-2004 and found out that high-rated portfolio generated higher returns as compared to the low-rated portfolio.  They concluded that the studies which compared and proved lower performance of socially responsible mutual funds fail to account for the fact that the performance of mutual funds depend to a large extent on the skills of the mutual fund manager and thus the results of these studies may not reflect the true picture of socially responsible investments.  David A. Sauer in his paper ‘The Impact of Social-Responsibility Screens on Investment Performance’ [2] compared the performance of a socially responsible portfolio with two unrestricted portfolio without taking into account the effects of transaction costs, management fees , etc on portfolio performance to more transparently examine the implications of restricted social investing on portfolio returns. His findings indicated that the social responsible screenings do not necessarily have an adverse impact on investment performance.

4. Impact Investing

While the above studies conclude that socially responsible investments do not underperform as compared to unrestricted investments and therefore should be preferred over unrestricted investment, a bigger question is that can capital markets bring about social change? One way a negative screening investment strategy does help in bringing about social change is by raising awareness about social concerns among socially unresponsive firms. As more and more people turn to SRI they can place pressure on these firms to change and become socially and environmentally responsible.

A more direct way of bringing about a social change is through impact investing. It is

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