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5% return with no risk or 10% return with 5% risk
katy123
Posts: 365 Forumite
This is a technical question i think....
WHich would you choose?
Can i simply conclude that the two investments carry the same expected value?
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,
WHich would you choose?
Can i simply conclude that the two investments carry the same expected value?
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,
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Comments
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risk is someone's opinion and not a matter of fact.
the banks had many many maths Ph.d working out the risks of their investments and they got it all wrong.
risk is a statistical object so if you invest lots of parcels of money is lots of investments then the 'value' may have a meaning; but if you invest just one (or a small number) parcel of money then 'value' means next to nothing.0 -
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If you are with the amounts above then I would go for £100.
If you times the numbers by 100 I would take the no risk...0 -
Can i simply conclude that the two investments carry the same expected value?
Are you asking if an investment with 5% return with a SD of 0% is on average equivalent to an investment with a 10% with a SD of 5%?
The answer is no: the 10% investment will on average yield 10%. Using a normal distribution it will return above 5% more than 84% of the time.
In the real world though an investment with an average return of 10% might well have standard deviations around 20% (68% of time returns will be in the region of -10% to +30%). They carry a very real chance of a loss in the short term.
Going back to your 'game show' example (100% chance of winning £50 or 50% chance of winning £100) - then yes: they have the same expected value. Some people will want the guaranteed money and others will take a gamble.
Let change the figures a bit and assume, for you that £500,000 would be a life-changing amount of money. You've done well in the quiz and can take a guaranteed £500K. Or you go double or nothing (£1M or £0). What do you do now? Both have the same expected value...0 -
JOn....i would take the £500k cos you said that i've done well (meaning that I've already probably answered a few correct answers), so I've already gained the £500k and was not risk free in the first place.
However, if i didn't have to answer any questions (gain the £500k) i would hesitate, the q is....is £500k alot to me????
Although i HATE it when ppl say follow your instinct.....i always try to remind myself that i should act logically and not emotionally, I'm learning slowly....so just to prove i am a logically person, i think i would opt to chance it...lol:):):)0 -
JOn....i would take the £500k cos you said that i've done well (meaning that I've already probably answered a few correct answers), so I've already gained the £500k and was not risk free in the first place.
From a probability perspective, it's now an independent event. You're effectively starting from a clean slate.
If you want a classic example of this then watch 'Deal or No Deal'. In some respects it's a banal program that's just about luck but it can be interesting from a probability and expectation perspective.However, if i didn't have to answer any questions (gain the £500k) i would hesitate, the q is....is £500k alot to me????
The banker is frequently offering contestants sums worth 50% (not 100%) of the expected value if then continued. Many people have a sum in mind that they find attractive and don't take the extra risk with the associated wild swings in their game equity.
Most contestants on there find £20k very tempting, never mind £500k (top prize is £250k as you probably know). If you're not sure if £500k is a lot then I must assume you're already very wealthy.0 -
I know what you mean. Technically it wound't matter cos both expected value are the the same £500k, so picking whichever should not make a diff.
How about this one? 500k and do one or £1.2m & nothing.
Which would YOU choose?0 -
I know what you mean. Technically it wound't matter cos both expected value are the the same £500k, so picking whichever should not make a diff.
My point is that it does matter if you can't mitigate the risk and taking the risk could have severe consequences (e.g. missing out on life-changing money).How about this one? 500k and do one or £1.2m & nothing.
Which would YOU choose?
I'd sell my position to an insurer or bookmaker for £550K
You can extend this even further. Most people could live incredibly well with £10M. Let's assume you're currently broke. You could have a guaranteed £10M. Or you could flip a coin and get either £0 or £250M (expected value £125M). Is it a no-brainer to go for the highest expectation? Or is a no-brainer to secure your financial future?0 -
In that second case it's a good call to sell your position again, this time for about £80-100M.My point is that it does matter if you can't mitigate the risk and taking the risk could have severe consequences (e.g. missing out on life-changing money).
I'd sell my position to an insurer or bookmaker for £550K
You can extend this even further. Most people could live incredibly well with £10M. Let's assume you're currently broke. You could have a guaranteed £10M. Or you could flip a coin and get either £0 or £250M (expected value £125M). Is it a no-brainer to go for the highest expectation? Or is a no-brainer to secure your financial future?
By the way, my girlfriend said she'd take the £10M and run. I'd probably do the same if I was given the choice. 50% chance of getting nothing when I already have £10M available risk-free just doesn't cut it for me. It would break my third golden rule to gamble away such a large amount.I am a Chartered Financial Planner
Anything I say on the forum is for discussion purposes only and should not be construed as personal financial advice. It is vitally important to do your own research before acting on information gathered from any users on this forum.0 -
This is a technical question i think....
WHich would you choose?
Can i simply conclude that the two investments carry the same expected value?
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.
A robot would presumably be programmed to minimise risk and therefore take the guaranteed payout. Taking on risk with no expected profit is pretty pointless. Although people do go to casinos, a robot would not.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,
You might want to read up on:
http://en.wikipedia.org/wiki/Kelly_criterion
How much to risk on such a bet depends on your bankroll and your advantage on the bet. In mathematical/gambling terms this bet is extremely low risk, and given the alternative between this and a 5% risk-free return, it would make sense to bet everything on it. (The Kelly criterion is often concerned more with things like betting £100 to win £5000 with probability of 1/40 - i.e. events that are quite unlikely to happen, but would translate to an expected profit in the long run)
10% return with a 5% standard deviation is much better than 5% guaranteed return, for pretty much everyone. That said investment returns are not normal, because you get an unusual number of large falls. This means the maximum loss you might reasonably expect is much lower than the normal distribution would imply.0
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