Anyone have any idea how to solve this?

[swimming]

I have been given this problem by one of the guys I work with and cannot for the life of me figure it out.

There is a stock with volatility \(\sigma\) and you are told to buy it over the course of the day. You are using the time weighted price over the course of the day as a benchmark. However, instead of executing the trade as told you execute the order at the opening price.

So what is your risk and return variance? In other words, if you sold the stock at the end of the day what is the variance of your return?

Anyone have any idea?

 

[Eugene Krel]

you are computing variance with a single data point?

 

[swimming]

i think you assume the stock follows a geometric brownian motion. i have no idea how to solve the problem though.

the answer is obviously supposed to be entirely theoretical, but i don't even know where to start.

 

[Eugene Krel]

why do you care about the stock model?

if you have a single execution your variance is 0.

 

[swimming]

i meant, if you buy the stock back at the end of the day what would be the risk and variance of the return?

 

[Sanket Patel]

i meant, if you buy the stock back at the end of the day what would be the risk and variance of the return?

Buy and hold any stock you want for, let's say, 10 years. I'll pay you 25x your realized variance and you pay me 6.25% on 10M, semiannually.

Deal?