Query on negative relationship between risk and reward.

[NewStudent]

In Chapter 11 : Investment strategy, Section 12.2 Competitive approaches - different perspectives on risk and reward, there are some pretty heavy concepts from Warren Buffet:

‘I would like to say one important thing about risk and reward. Sometimes risk and reward are correlated in a positive fashion. If someone were to say to me, I have here a six-shooter [a type of gun] and I have slipped one cartridge into it. Why don't you just spin it and pull it once? If you survive, I will give you $1 million.' I would decline - perhaps stating that $1 million is not enough. Then he might offer me $5 million to pull the trigger twice – now that would be a positive correlation between risk and reward!
The exact opposite is true with value investing. If you buy a dollar bill for 60 cents, it's riskier than if you buy a dollar bill for 40 cents, but the expectation of reward is greater in the latter case. The greater the potential for reward in the value portfolio, the less risk there is.'

Then there is also IFoA Explanation pointing out a technical flaw :
If everyone in the market knew and agreed that it was really a dollar bill, its price would be exactly one dollar. The only way a dollar would be available for sale for less than one dollar is if there was some uncertainty over whether it really was a dollar (perhaps it is a fake), and the cheaper it is offered for sale, the less likely it is that it really is a dollar. Once the quote is adjusted for that, the ‘expected’ pattern of higher risk demanding higher reward is restored.

So, I have below doubts:

1. How is Russian roulette relevant in this context ?
2. In value investing why is there a negative relationship between risk and reward ?
3. Specifically, a) why is the expectation of reward is greater when a dollar bill is bought for 40 cents than 60 cents and
b) the risk higher when a dollar bill is bought for 60 cents rather than 40 cents ?
4. Can you provide additional comment / explanation on IFoA's explanation ?


Also, are students required in exams to do comments / analysis on such deep philosophical / contemplative issues ? Because when I see such issues, my mind becomes blank for further ideas.


Note: For Russian roulette game, as per Wikipedia
After a single spin, the probability of it firing is 1⁄6, followed by 1⁄5 on the second pull, 1⁄4 on the 3rd pull and so on, until if it failed to fire 5 times, the probability is 1⁄1 (=1) on the final pull. If the cylinder is re-spun after each trigger pull, the probability of firing remains 1 in 6 on each occasion, and the probability of it having fired after 6 pulls is

, or about 66.5%.

So why not simply multiply the probability of survival with monetary reward, to find the expected reward.
Can you also state the correct probabilities and expected rewards in both situations?

 

[Colin McKee]

Hmmm. Good point. I can answer your point below the numbered questions first: no, there have never been any SA6 or SA7 questions that ask for actual quotes or award marks for real life examples given in the core reading. They are there to enhance the readers enjoyment I think. I can also say that you probabilities look fine, although I am unlikely to test the maths with a real life experiment.
1. How is Russian roulette relevant in this context ?
I think its just demonstrating the link between risk and reward. The risk of dying is always the same, but for some return (£1m? £5m?) you might take the risk. So risk and reward are positively correlated.

2. In value investing why is there a negative relationship between risk and reward ?
Buffet is saying that all share investments are just companies. Value shares have a cheap price because they are unloved, growth shares have a high price because of high expectations, but Buffet thinks you are buying the same thing but just paying a higher price for it. If you pay 40 cents for a dollar rather than 60 then your transaction is less risky - ie you have sunk less of your wealth into the transaction, but getting the same thing (which may be a dollar and may be a dud). So risk and return are on their heads - growth shares are high priced and therefore offer the lowest prospective return, but the risk is higher because you are paying a high price ??

3. Specifically, a) why is the expectation of reward is greater when a dollar bill is bought for 40 cents than 60 cents and
b) the risk higher when a dollar bill is bought for 60 cents rather than 40 cents ?

This is explained above I think. 40 cents will rise more when its true dollar worth is realised. So higher return.

4. Can you provide additional comment / explanation on IFoA's explanation ?

So the IFoA are saying that if you believe Buffet, (a dollar is a dollar, so a company is a company whether its value of growth - they are just the same) then you are taking more risk when you buy the expensive one. But if you think they might be fakes (so a cheap value company is cheap because its duff) then you may well get a better return from the growth investment. So a dollar may be a real one or a (value share) fake. In these circumstances, there may be more risk with the cheaper investment.

I must admit, I dont think I have ever got into the detail of these quotes before, but I quite like them now.