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De-constructing Dazzling Diversification

I mentioned in a previous post that one of the important features of becoming a multimillionaire is diversification. Without going too technical, here is a brief definition of diversification from the Wikipedia article on the subject:

“Diversification means reducing risk by investing in a variety of assets. If the asset values do not move up and down in perfect synchrony, a diversified portfolio will have less risk than the weighted average risk of its constituent assets, and often less risk than the least risky of its constituents.”
– Wikipedia, “Diversification in finance

It is not immediately intuitive how diversification of assets, that is, having multiple income streams will reduce your risk whilst keeping your expected returns constant. Here I present a little story to demonstrate the benefits of diversification.

Diversification Scenarios & Examples

SCENARIO 1: You’re on a game-show and the host offers two choices:

“I am going to flip one coin. If it’s heads you get $10,000. If it’s tails you leave with nothing. Alternatively, I won’t flip the coin and you can have $4,000 now?”

What does one do? Some people take the money and run, preferring to have something guaranteed, rather than risk getting nothing. Other people figure that they came with nothing and might as well take the chance to walk away with $10,000.

Furthermore, your expected pay-off from the coin flip is $5,000 (1/2 X $0 + 1/2 X $10,000). Since this is $1,000 more than the $4,000 guaranteed this person will take the gamble.

SCENARIO 2: You’re on a game-show and the host offers two choices:

“I am going to flip ten coins. Each coin will be worth $1,000 if it lands on heads. If the coin doesn’t land on heads then you get nothing from that coin only. Alternatively, I won’t flip the coins and you can have $4,000 now?”

What do you do? This scenario appears very different. Some people reason, I now have ten chances to get $1,000 at least so I’m very unlikely to walk away with nothing, I might as well take the gamble. Other people may disagree and argue that they would still rather have $4,000 guaranteed.

Diversification Discussion

Theoretically, your pay-off in scenario 2 does not change from scenario 1. You’re still expected to get $5,000 from the gamble (1/2 X $1,000 + 1/2 X $1,000 + 1/2 X $1,000 + 1/2 X $1,000 + 1/2 X $1,000 + 1/2 X $1,000 + 1/2 X $1,000 + 1/2 X $1,000 + 1/2 X $1,000 + 1/2 X $1,000). However, I guarantee that more people were willing to take the gamble in scenario 2 than in scenario 1.

Why is this the case even though your expected pay-off does not change?

It is because in the second scenario the previous risk has been spread across 10 different assets rather than risk it all in one go. Of course your returns may not be as high as the first gamble but then again your losses are not as low. This is the benefit of diversification. It helps sustain wealth across many different outcomes.

Did you take both gambles? Let us know in the comments!

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