Question 5.87

57. The yearly rate of return on the Standard & Poor’s 500 (an index of 500 large-cap corporations) is approximately normal. From January 1, 1960, through December 31, 2009, the S&P 500 had a mean yearly return of 10.98%, with a standard deviation of about 17.46%. Take this normal distribution to be the distribution of yearly returns over a long period.

  1. In what interval do the middle 95% of all yearly returns lie?
  2. Stocks can go down as well as up. What are the worst 2.5% of annual returns?

57.

(a) , or to 45.90% (see diagram)

(b) A loss of at least 23.94%

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