Understanding Uncertainty & Risk

Are you a risk taker? Or a risk avoider? Do you like to bet all you have (All in as they say in poker) for a big payoff, or do you like to play safe and actively seek to avoid risk? Most of us lie somewhere in the beginning.

If risk is only about avoiding uncertainty, then it is no brainer of a choice. There is a lot of risk and nothing to gain in walking blindfolded across NH5. However in most cases risk is tied to return and when we reduce risk we also reduce return. How do we make such choices? Lets play a simple game.

We spin a coin. If it is heads we win Rs 100 If it is tails we win nothing. Simple math tells us that the expected value is Rs 50. Call this game 1

In Game 2, you win Rs 50 if it is Heads, and Rs 30 if it is Tails. The expected value is Rs 40, which is less than game 1.

But if given a choice, which game would you like to play? Game 1 has a higher expected value. However Game 2 is more attractive to the risk averse.

If you think you would choose Game 1, (after all it is a small sum) what if I add a few zeroes to the figures? Now take a look at the Table below

Option A (prob & Payoff) Exp Value Option B (prob & Payoff) Exp Value
20% of 400 80% of 300 320 20% of 700 80% of 100 220
40% of 400 60% of 300 340 40% of 700 60% of 100 340
50% of 400 50% of 300 350 50% of 700 50% of 100 400
60% of 400 40% of 300 360 60% of 700 40% of 100 460
80% of 400 20% of 300 380 80% of 700 20% of 100 580
100% of 400 0% of 300 400 100% of 700 0% of 100 700

It is obvious that in the first row, you are better off with Option A. As you go down the table, Option B starts looking better and better. In the last row, clearly option B is Rs 700 straight into your pocket. However the key is where do you make the switch from Option A to Option B.

Probability dictates that Option B is better from row 3 onwards. However the worst-case scenario in Option A is better, you are assured of a min amount of Rs 350. In Option B, you have a chance that you will end up with only Rs 100. What would you choose? Most of us are risk averse and would choose option A.

On the other hand, the best-case scenario in option A is a mere 400 compared to Rs 700 in option B. A risk taker would probably take option B, even in row 2 and maybe row 1 also. So do you focus on the best case or the worst case?

Nothing wrong, of course in being risk averse. We need to understand our comfort level with risk and make economic choices accordingly. The more risk averse we are the more we are willing to give up to reduce variations in outcome.

The level of risk that one is willing to assume is also dependent on the environment. However, in some situations, people are risk averse to the point of being irrational.

For example, in an experiment, participants were asked how much they were willing to pay for a lottery ticket which has two prizes – a 50% chance of winning $50 and a 50% chance of winning $100. Obviously, it was expected that people would pay between $50 and $100 (the expected value being $ 75). Stunningly the average bid was $16 with a median of $5.

Crazy, as the minimum you would win was $50. However what we understand from this and similar experiments are that people simply dislike uncertainty.

Say, you are running a restaurant, which can seat 200 people during lunch hour. The average customers that you get are also 200, which is perfect. Or is it? One must also consider variance. Suppose you get as few as 100 customers a day and as many as 300 a day. When you get 100 you lose revenue as most of the costs like rent, salaries etc are the same. When you get 300 customers, you have to turn away 100, which is lost revenue and also creates ill will among customers.

Different businesses have different capacities (and strategies) for absorbing risk. However most of us would prefer steady predictable revenue like a salary. That is why most of us are willing to forgo a higher average – a higher expected value – in exchange for a steadier payout

We understand the desire of students (and parents) to get a secure government job even if it doesn’t pay as much as a private sector alternative. It is difficult for us to even imagine the number of people who sit for an SBI PO or Clerical exam, way more than the number of people who sit for the CAT or even the IIT JEE.

What are the ways of reducing this uncertainty?

  • Avoid risk altogether (eg: Stick to Bank FD’s & Govt Securities)
  • Reduce risk by pooling the risk (spreading the risk)
  • Reduce risk by increasing our knowledge about the situation
  • Transfer the risk to someone else (Insurance)

Avoiding risk altogether is a bad idea, as it leads to significant loss of opportunity. By staying off the roads for life you bring the risk of dying in an accident down to zero but clearly by paying a huge cost.

Rahul Reddy

Director Vanguard Bschool

www.vanguardbschool.com

Understanding Uncertainty & Risk
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