5% return with no risk or 10% return with 5% risk

[bullboy8]

This is a technical question i think....

For example, in a game show i offer two options:
first option- 2 doors, one with £100 and one with £0,
second option- take £50 and leave

for risk averse people they will take the £50 and leave but the two options carry the same expected value of £50 so if a robot was to choose, it would choose either one.

Can this same "expected value" be applied to investments which are in % instead of values? for example, when I use the 10% return minus the 5% risk = 5%. The risk is the number derived from SD, so i'm thinking whether or not this will work. 1 SD is 68% of the time you will achieve between 5-15% of the return for opting for the 10% expected return investment,

 

[Jemima]

yeah but... the first option has expectancy of $50 and the risk that you might bot get any money, ever. The second option you are promised $50.

it's like saying "do you want $50 definately or probably?".

they havent got the same utility.

 

[mb325]

yeah but... the first option has expectancy of $50 and the risk that you might bot get any money, ever. The second option you are promised $50.

it's like saying "do you want $50 definately or probably?".

they havent got the same utility.

That depends on an individual's utility curve...

In respect to the original question surely the probability of gaining 10% vs losing 5% will play a part. If it's 50:50 then on a £100 account the expected return of option 2 is £102.5. If the likelihood of a 10% gain increases though then expected return increases and so option 2 > option 1.

 

[Jemima]

for the first option to be the better investment, it needs to reward the investor more than option two.

It doesn't.

 

[bullboy8]

just to make it clear, the 10% expected return is a one point return (assume the distritbution is bell shaped) then 68% of returns will fall within 5%-15 return. It is NOT 50% chance of getting 5% return or 50% chance of getting 10% return.

 

[mb325]

just to make it clear, the 10% expected return is a one point return (assume the distritbution is bell shaped) then 68% of returns will fall within 5%-15 return. It is NOT 50% chance of getting 5% return or 50% chance of getting 10% return.

ah, sorry i completely missed that part of the question :whistling

 

[bullboy8]

i think this is my conclusion...

the expected return of 10% is the geometric average and therefore does not consider the volatility of a share. SO say i used the last 100 years returns and came up with a geometric annual return of 10% that does not tell me what the volatility was during that period. yes, the risk free rate is 5% giving me a risk premium of 5%, so surely i should invest as i would either get 5% or 10% (only for the latter to be volatile, but isn't it the destination that is important and not the route? But, surely i need to consider volatility (cos that is the risk) but why should i if over 100 years the return has been 10%? (5% more?????)

lol....thanks for the input guys