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PITTM
08-07-2005, 06:03 PM
your investment has a .7 chance of doubling after a year and a .3 chance of halving after a year. what is the SD on the ROR?

rj

Luzion
08-07-2005, 09:28 PM
[ QUOTE ]
your investment has a .7 chance of doubling after a year and a .3 chance of halving after a year. what is the SD on the ROR?

rj

[/ QUOTE ]

Havent done this in awhile, but Ill try to help.

Investment 0.5x 2x
p(x) 0.3 0.7

E(x) = 0.5(0.3) + 2(0.7) = 1.55x
E(X^2) = (0.3)\$50^2 + (0.7)(\$200)^2 = 2.875x
V(X) = 2.875 - 1.55^2 = .4725x

SD = sqrt(.4725) = .68739x

Hope thats what you are looking for...

BruceZ
08-07-2005, 09:48 PM
[ QUOTE ]
E(x) = 0.5(0.3) + 2(0.7) = 1.55x

[/ QUOTE ]

E(x) = -0.5(0.3) + 1*(0.7) = 0.55

E(x) is the average gain as a fraction of the principle.

[ QUOTE ]
E(X^2) = (0.3)\$50^2 + (0.7)(\$200)^2 = 2.875x

[/ QUOTE ]

E(x^2) = (0.3)*(0.5)^2 + (0.7)*(1)^2 = 0.775

[ QUOTE ]
V(X) = 2.875 - 1.55^2 = .4725x

[/ QUOTE ]

V(x) = 0.775 - 0.55<font color="red">^2 = 0.4725 SAME </font>

[ QUOTE ]
SD = sqrt(.4725) = .68739x

[/ QUOTE ]

SD = sqrt(<font color="red">0.4725) =~ 68.74% SAME</font>

This is the standard deviation of the return on investment, as a percent of the principle.

Luzion
08-07-2005, 09:58 PM
[ QUOTE ]
E(x) = -0.5(0.3) + 1*(0.7) = 0.55
E(x^2) = (0.3)*(0.5)^2 + (0.7)*(1)^2 = 0.775

[/ QUOTE ]

Ok, you can approach it like that if you wish.

Your answer is +0.55% of the investment. Mine is x = investment. Answer = 1.55x investment. Same result. I shouldnt talk though since I havent done probability for finance yet so I dont know standard notation....:(

[ QUOTE ]
V(x) = 0.775 - 0.55 = 0.225

[/ QUOTE ]

V(X) = E(X^2) - E(X)^2

You forgot to square your mean

Should be 0.775 - 0.55^2 = 0.4725

[ QUOTE ]
sqrt(0.225) =~ 47.43%

[/ QUOTE ]

sqrt(0.4725) = 0.68739

so we both get the same answer /images/graemlins/grin.gif

BruceZ
08-07-2005, 10:14 PM
[ QUOTE ]
[ QUOTE ]
E(x) = -0.5(0.3) + 1*(0.7) = 0.55
E(x^2) = (0.3)*(0.5)^2 + (0.7)*(1)^2 = 0.775

[/ QUOTE ]

Ok, you can approach it like that if you wish

Your answer is +0.55% of the investment. Mine is x = investment. Answer = 1.55x investment. Same result. I shouldnt talk though since I havent done probability for finance yet so I dont know standard notation....:(

[ QUOTE ]
V(x) = 0.775 - 0.55 = 0.225

[/ QUOTE ]

V(X) = E(X^2) - E(X)^2

You forgot to square your mean

Should be 0.775 - 0.55^2 = 0.4725

[ QUOTE ]
sqrt(0.225) =~ 47.43%

[/ QUOTE ]

sqrt(0.4725) = 0.68739

so we both get the same answer /images/graemlins/grin.gif

[/ QUOTE ]

Yeah, I was still fiddling with it, so I went back and made the changes in red. Your E(x) is the expected value of the final amount, whereas mine is the expected value of the gain, or what we normally refer to as the EV. Yours is consistent throughout, so it's fine.