Probability quiz:
>There is an asset whose price goes up 30% with 50% probability
>It goes down 25% with 50% probability
>After thousands of iterations of these prices changes, what is the expected return?
Well what is it?
Probability quiz:
Michael Bell
Adrian Phillips
Depends on the order it goes up and down. Even assuming it goes up 500 times and down 500 times it would still depend when the end amount is after each change. What if it goes up 8 times in a row, then down 20, then up 45, then down 200? Not enough info to answer.
Andrew Wright
The answer is that the value of the asset would in theory tend towards zero. Given the 50/50 chance, the expected asset value at each turn is 0.975 of the previous asset value
Ayden Reed
nerd
Ian Phillips
>the expected asset value at each turn is 0.975 of the previous asset value
Think again. 0.5 * (1.3 + 0.73) is 1.025.
Dominic Torres
nerd
Dominic Torres
Pretend each outcome occurs weighted by chance of occurrence:
b = (1.3 * 0.5 + 0.75 * 0.5) = 1.025 = 2.5% expected return per iteration
Play 1000 expected iterations with expected base b to calculate expected outcome
b^1000 = 52949930179 times return (approx)
Matthew Torres
no
Expected value grows exponetially assuming that the increases are independent.
Jordan Scott
Anyone who thinks the asset grows is an idiot, you can literally do it yourself to check
100 x (1.3 or 0.75) in as many combinations as you want, maintaining a 50/50 frequency of each
Tyler Barnes
just checked. this user is correct; the total inevitably depreciates
Julian Myers
>I don't know what expected value means
are you american by chance?
Jeremiah Robinson
This.
Matthew Brown
u don't need to be a nerd for this. everyone knows that if u lose 50%, u need 100% to break even. if u lose 25% ... u need to make 33.3% to break even. if we're only gaining 30% on average for every 25% loss, we're losing money and trending toward 0.
Oliver Garcia
-100%
1.3*0.75 < 1
(
Hunter Lewis
Ok listen fucktards. I know math his hard, so here have simple explaination:
We are not talking about what happens on average. We are not talking about what happens when the expected coin-tosses happen. We are talking about expected value. This term means something. You can look it up if you're not scared of high school math.
Anyway. The reason the expected value grows exponentially is that if you get lucky a lot, the reward grows exponentially. Even though these scenarios are very unlikely, their winnings are so extreme that they screw the expected value of the whole game.
Here's some idiot-proof script that illustrates it. You can run it in your browser
var max = 1;
var roundResult = 1;
var sum = 0;
for(var round = 0; round < 1000; round++){
roundResult = 1
for(var i = 0; i < 1000; i++){
if(Math.random()*2
Isaiah Ortiz
I just did 1000 simulations with 100 iterations in each simulation. My code is here: pastebin.com
Mean return: 1016.00%
Median return: -71.80%
Most simulations lost money because 1.3*0.75 = .975 < 1. However, the simulations which got lucky had exponential growth, so their returns were high enough to skew the mean.
Xavier Ortiz
>it take 100% gain to offset a 50% loss
Just extrapolate this concept to anything of this nature.
John Sanders
> the expected asset value at each turn is 0.975 of the previous asset value
Wrong. It is 1.025 times the previous asset value.
Expected return with 1 iteration = .5*1.3 + .5*.75 = 1.025
Expected return with 2 iterations = .25*(1.3^2) + .5*1.3*.75 + .25*(.75^2) = 1.050625
The math above is just summing up the probability of each outcome * the return of that outcome. Amusingly, 1.050625 = 1.025^2
A modified version of the code I linked to in backs this up. With 1,000,000 simulations, the mean simulated returns are all within .01 of what they theoretically should be.
Mean return with 1 iterations: 1.025
Mean return with 2 iterations: 1.051
Mean return with 3 iterations: 1.076
Mean return with 4 iterations: 1.103
Mean return with 5 iterations: 1.131
Mean return with 6 iterations: 1.160
Mean return with 7 iterations: 1.189
Mean return with 8 iterations: 1.218
Mean return with 9 iterations: 1.250
Mean return with 10 iterations: 1.282
Gavin Edwards
You are a retard.
Jace Campbell
Oh boy.. when do we tell him guys?
Michael Bennett
you don't need to write a simulation to see that but he's right.
learn what an expected value is.
Aiden Reed
-99.99999...%
Elijah Reyes
the fuck
correct answer
i think you need to check your math and/or run some simulations, dawg. just because it's up 30 vs down 25 (and 30 > 25) doesn't mean you're gaining.
think about this. up 50%, down 50%. $100 goes up to $150, down to $75. if the events happen in the other direction, the same thing happens ($100 -> down to $50, up to $75).
this is why people say things like "oh man if the stock market goes down 75% you have to make 300% gains to make it back"
Isaiah Perry
Underrated
Lincoln Diaz
2.5%
Aaron White
>think about this. up 50%, down 50%. $100 goes up to $150, down to $75
The problem with your reasoning is that there is no guarantee that it will go up and down an equal number of times.
The situation you are describing is the same as OP's question, but at each iteration, there is a 50% chance of making a 50% gain and a 50% chance of taking a 50% loss.
With two iterations, there are 4 equally likely outcomes.
"up up" results in a return of 1.5*1.5 = 2.25
"up down" results in a return of 1.5*.5 = .75
"down up" results in a return of .5*1.5 = .75
"down down" results in a return of .5*.5 = .25
The average return in this scenario is (2.25 + .75 + .75 + .25)/4 = 1. This means that on average you won't gain or loose anything despite the fact that there is a 75% chance that you will loose money.
OP's scenario is very similar. With two iterations, there are 4 equally likely outcomes.
"up up" results in a return of 1.3*1.3 = 1.69
"up down" results in a return of 1.3*.75 = .975
"down up" results in a return of .75*1.3 = .975
"down down" results in a return of .75*.75 = .5625
The average return in this scenario is (1.69 + .975 + .975 + .5625)/4 = 1.050625. This means that on average you will have a 5.06% profit after 2 iterations.
The number of people in this thread who don't know how to compute expected values is fucking depressing. Please read en.wikipedia.org
Brody Butler
> not coding a markovian chain with those probabilities and then running a billion monte carlo sims via MCMC just to answer OP's question
where the fuck are all the autists at yo?? no wonder this board is fucking dead as fuck and bleeding money
Noah Butler
I've been sperging out pretty hard. Did you read or ? I was using a Markov chain (albeit a very simple one) to do millions of simulations. I'm not the only one who did simulations either. did too.
John Edwards
-100%
Adrian Gutierrez
If X_{i} (i = 1,...,n) are independent random variables with P(X_{i} = 1,3) = P(X_{i} = 0,75) = 0,5, then the expected value of X_{1} is E[X_{1}]=0,5*(1,3+0,75) = 1,025.
The expected value of the product X_{1}*...*X_{n} is just the product of the expected values, because the X_{i} are independent. So
E[X_{1}*...*X_{n}] = E[X_{1}]*...*E[X_{n}] = 1.025^n
The expected value grows exponentially, because the long tail of the distribution (where you win a lot more than you lose) more than compensates for the cases where you lose money.
pic related is the definition of expected value
Lincoln Taylor
beat me to it
Also from investopedia.com
>Expected return is the profit or loss an investor anticipates on an investment that has known or expected rates of return. It is calculated by multiplying potential outcomes by the chances of them occurring and then summing these results. For example, if an investment has a 50% chance of gaining 20% and a 50% change of losing 10%, the expected return is (50% * 20% + 50% * -10%), or 5%.
Thomas Nguyen
>The expected value of the product X_{1}*...*X_{n} is just the product of the expected values, because the X_{i} are independent.
If anyone (like me) is wondering why this is true, en.wikipedia.org
Christian Morris
You guys aren't calculating the expected value right.
Imagine it was a 100% gain and a 50% loss with 50/50 probability.
(50% * 100% + 50% * -50%) = 25%
It should be a 0% gain on average.
Chase Rogers
It goes to zero you dumb virgins
Joshua Phillips
Camden Barnes
chad
Levi Morgan
Gavin Diaz
100*1.3=130 30gain
130*.25=97.5 32.5 loss
damn numbers, u scary
wheres that pic with percent losses and percent gains needed for initial investment
Lincoln Ross
Jack Ortiz
You need to do multiple simulations. It will drop to 0 almost every time, but the few that increase in value will increase a ton. The more iterations in each simulation, the more dramatic this behavior becomes. Overall, doing more iterations increases the mean return but decreases the probability of a net increase.
Hunter Moore
This is because it will converge almost surely to 0 but it will blow up in L^1 norm.