# stat questions

A stock increased in value last year. Which will be greater, its continuously compounded or its holding period return? A) its holding period return B) Neither, they will be equal C) Its continuously compounded return. I put C, the answer was A. What did they mean by continuously compounded return? I basically said if an HPY has a return of 40% (16.8/12 -1 ) then 40% continuously compounded is (1+.40/365)^365 - 1 = 49% which is higher. Was this the wrong equation? second question Monthly sales of hot water heaters are approximately normally distributed with a mean of 21 and a standard devitation of 5. What is the probability of selling 12 hot water heaters or less next month? A) 1.80% B) 96.41% C) 3.59% Z= (12-21)/ 5 = -1.8 answer is C I didn’t have a negative z table to look at so instead I looked at a positive z table of 1.8 and it was 96.41%. 100-96.41% is the answer C. I was just wondering what this means. Is the 96.41% saying that the probability of selling 30 hotdogs or less (30-21/5 = pos 1.8) is 96.41% and the probability of selling 12 or less is 3.59%?

Question 1: To calculate Continuously Compounding Rate, 1. Get the Annualized Rate from HPY as (.40 / no of days in the holding period) * 365 2. Then Continuous Compounding Rate = ln(1 + Annualized Rate) Question 2: “Is the 96.41% saying that the probability of selling 30 hotdogs or less (30-21/5 = pos 1.8) is 96.41% and the probability of selling 12 or less is 3.59%?” Yes, this understanding is correct.

i see, thank you. So what is the difference between the LN(1+annual) and the equation I used?

In your calculation, you were attempting to calculate daily compounding. Whereas, countinous compounding is compounding your rates with every nano second or even less.

I see thank you!

-------------- I basically said if an HPY has a return of 40% (16.8/12 -1 ) then 40% continuously compounded is (1+.40/365)^365 - 1 = 49% which is higher. Was this the wrong equation? -------------- If you say 40% is the HPY, then you need to us ln(1.4) because it finds “what rate, if continuously compounded, results in a 40% return”. That rate is 33.647…%. e^.33647 = 1.4 What you were doing above is taking the HPY and compounding it even further.