Question

There is a probability of 0.63 that there will be extremely cold weather this coming Winter. If it does, we expect investors of Star \& Bucks to achieve a return of 0.15 . Else, investors may expect a lower return of 0.04 . Can you estimate the variance of this rate of return? Type your answer as decimal (i.e. 0.052 and not 5.2\%). Round your answer to the nearest four decimals if needed.

Answer 1

The estimated variance of the rate of return for Star & Bucks investors is 0.0028, considering the given probabilities for different weather conditions and corresponding returns.

Step-by-step explanation:

To estimate the variance of the rate of return for Star & Bucks investors, given the probabilities of different weather conditions, we use the formula for the expected value (E) and the variance (VAR) of the returns. The expected value is the sum of all possible returns weighted by their probability, and the variance measures the spread of these returns.

The expected return (E) can be calculated as follows:

• 
  
• E = (Probability of extremely cold weather) * (Return if cold) + (Probability of not cold weather) * (Return if not cold)
• 
  
• E = (0.63 * 0.15) + (0.37 * 0.04)
• 
  
• E = 0.0945 + 0.0148
• 
  
• E = 0.1093

Now, to calculate the variance (VAR), we use the following steps:

• 
  
• Variance = (Probability of extremely cold weather) * (Return if cold - E)² + (Probability of not cold weather) * (Return if not cold - E)²
• 
  
• Variance = (0.63 * (0.15 - 0.1093)²) + (0.37 * (0.04 - 0.1093)²)
• 
  
• Variance = (0.63 * 0.00164564) + (0.37 * 0.00481649)
• 
  
• Variance = 0.00103715 + 0.00178199
• 
  
• Variance = 0.00281914

Therefore, the estimated variance of the rate of return is 0.0028 when rounded to four decimal places.