Behavioural Finance - the answers...

In my previous entry, i've posted a question developed by Kahneman & Tversky. Here's the question again:-

#Choose 1 from (a) (b) and 1 from (c) (d) the following

(a) A sure chance of getting $2,400, or
(b) A 25% chance of getting $10,000 and a 75% chance of getting nothing.

(c) A sure chance of losing $7,500, or
(d) A 25% chance of losing nothing and a 75% chance of losing $10,000 #

Ok, generally, normal people, like you and me will choose (a) and (d). Why?

The efficient market theory assumes that all investors are Rational, i.e. we will always allocate our assets according to Expected Return and Risks. A rational investor will always go for the asset with the highest expected return, at a given level or risk, or invest in the asset with the lowest level of risk, at a given level of expected return. That's the theory.

In reality, we're no where near that. We are rather emotional. Ok, back to the question. Why choose (a) over (b)?

We will generally choose (a) because (a) gives you a 100% chance of receiving $2,400 bucks! A windfall! Whereas in (b), you have to gamble for it. So your mind has already been anchored that you can get $2,400 for sure, why gamble for it? But, in terms of finance, the way we generally look at it is through the calculation of Expected Return.

In (a), the expected return is $2,400.
In (b), the expected return is [0.25 x $10,000] + [0.75 x $0] = $2,500

Since (b) has the higher expected return comparing to (a), (b) should be chosen instead!

Ok, how about (c) and (d)?

Most people, including myself, Hate Losing. Let it be sports, card games, in relationship & investing, we dislike losing. Most people will choose (d) over (c), why?

Basically, (c) tells you, “You are a confirm loser. Pay me $7,500 now!” This is painful. (Both emotionally and financially)
So you say, “Hey, I am not a loser, I will choose (d) and I am not going down without fighting!”

Some academics say investors always believe too much in his/herself, i.e. Over-confidence. Oh well, we will eventually be humbled by the market…

Anyway, so you chose (d). Let’s do some calculation.

In (c), the expected return is -$7,500
In (d), the expected return is [0.25 x $0] + [0.75 x -$10,000] = -$7,500

Well, in this case, a rational investor should be indifferent between (c) and (d), but of course in reality, most of us hate losing and always over-confident that we might be lucky this time, (d) will be the favourite for sure.

So, if I combine all four of them together, which two is the best combination?

Let’s start with combination (a) & (d), the top picks by most people. The total expected return is

E(R) = [1 x $2,400] + [0.25 x $0] + [0.75 x -$10,000] = a loss of $5,100. Ouch!

According to Kahneman & Tversky, the optimal combination is (b) & (c) [or (d)]!

Here’s the expected return

E(R) = [0.25 x $10,000] + [0.75 x $0] + [-$7,500] = a loss of $5,000, effectively $100 better off than the (a) & (d) combination.

So what does this tell us?

Most people, like you and me, have mind-framing in our decision making process. We always differentiate the decision making process of “realizing gains” & “realizing loss”. In terms of gain, we always want the safest bet, unless, you have some buffer to gamble. Whereas, for loss, we prefer to gamble, and who knows, we might be lucky and can get away with lesser losses?

We rarely combine those two decisions together, although we should.

That’s the mentality of general investors ;)