Calculating probability that a stock gained value and lost value

The major stock market indexes had mixed results in 2011. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was 0.00%. The mean one-year return for the NASDAQ, a group of 3,200 small and medium-sized companies, was -1.8% Historically, the one-year returns are approximately normally distributed, the standard deviation in the S&P 500 is approximately 20%, and the standard deviation in the NASDAQ is approximately 30%.
a. What is the probability that a stock in the S&P 500 gained value in 2011?
b. What is the probability that a stock in the S&P 500 gained 10% or more in 2011?
c. What is the probability that a stock in the S&P 500 lost 20% or more in 2011?
d. What is the probability that a stock in the S&P 500 lost 40% or more in 2011?
e. Repeat a - d for a stock in the NASDAQ.
f. Discuss the risks associated with a large standard deviation.

Solution Preview

For S&P 500, mean=0 and sd=20. SInce one-year returns are approximately normally distributed, z=(x-mean)/[sd]=(x-0)/[20].

a. P(a stock in the S&P 500 gained value in 2011)=P(X>0)=P(Z>0/20)=P(Z>0)=0.5 from standard normal table

b. P(a stock in the S&P 500 gained 10% or more in 2011)=P(X>10)=P(Z>10/20)=P(Z>0.5)=0.3085 from standard normal table

c. P(a stock in the S&P 500 lost 20% or more in ...

Solution Summary

The solution gives detailed steps on calculating the probability that a stock gained value and that a stock lost value.

... of a fair market is 0.4, and the probability of a ... average rate of return, multiply the probabilities by the ... in the problem above, you can calculate the average ...

... of variation CV (8-4) return; calculated as r ... If we calculate the coefficients of variation for ... manual for instructions on calculating historical standard ...

...Calculates portfolio's return, standard deviation etc. ... rf= 3.75 % calculated above βA= 1.8 rm= 14% rA ... remaining values in the equation we calculate the return ...

... explain how expected returns can be calculated given the ...Probability of Earning Rate of Return Products (1 ... When investing in the corporate stocks, the investor ...

... x Difference Prob x Difference 2 Probability from mean ... Step 1: calculate the weights of the stock in the ... to market, further loss/ gain is calculated from this ...

... (DO NOT CALCULATE THE STANDARD DEVIATIONS! ... 272 * 3% = 8.16 Binomial Probabilities. Data Sample size 7 Probability of an event of interest 0.5. ...

... the compounding frequency and is calculated as for ... 7. Consider the problem of calculating a loan ... 21. Consider the probability distribution of rate of return on ...

... 3. Calculate the Accrued Interest: Accrued interest is the fraction ... It is calculated by the following formula: ... In all probability the seller of the call option ...

... a bull market does not offer a high probability of success ... theory uses a discount rate to calculate rate of ... Wedging is a clue the stock will break downward in ...