Because of the outbreak of Covid-19, the S&P 500 stock index fell over 30% from its recent high level. At the same time, the volatility index of the S&P 500 (a measure of the market's expectation of 30-day forward-looking volatility) spiked from 14 to 80. Assume that in December 2019 (before the outbreak of the Covid-19) the expected growth rate of the index was 5%, the discount rate was 10%, and the risk-free rate of return was 3.5%. Also, assume that investors maintain the same Sharpe ratio before and after the outbreak.

a) Evaluate the following statements and support your evaluation with relevant calculations and/or derivations. .

1.The fall of the index is the result of a permanent change in the expected future growth rate caused by the virus. (2 pts)

2.The fall of the index is the result of a permanent change in future cash flows of the companies included in the index. (2 pts)

3.The fall of the index is the result of a permanent change of volatility in the market. (3 pts)

4.The fall of the index is the result of a deferral of future cash flows of US companies for a certain number of periods. (3 pts)

b) Propose possible explanations for the fall of the index; do you think such price movements triggered by the outbreak of the virus are rational? Explain carefully. (7 pts)