INR-USD exchange rate

The INR-USD exchange rate has been in news for the last few weeks. The question in every one mind seems to be how low can it go? What is the chance that it would cross  INR 60 per USD  in the next three months?

Based on the last 10 years data it seems that the chance of rupee breaching the INR 60 per USD mark is 13.5%. That's about 1 in 7. Quite possible in other words.

The chance of it crossing INR 62 per USD in the next three months is about 1%.

In his article "Optimum Strategies for Creativity and Longevity" Dr. Sing Lin gives an interesting actuarial table of Retirement Age and Age at Death which is reproduced below:

Retirement Age		Age at Death
49.9		86
51.2		85.3
52.5		84.6
53.8		83.9
55.1		83.2
56.4		82.5
57.2		81.4
58.3		80
59.2		78.5
60.1		76.8
61		74.5
62.1		71.8
63.1		69.3
64.1		67.9
65.2		66.8

A quadratic regression model can be nicely fitted to this data:

Age of Death = - 121.2 + 8.335 Retirement Age - 0.08394 Retirement Age**2

S = 0.713363 R-Sq = 99.0% R-Sq(adj) = 98.8%

It seems that one should plan to retire by 58 or 60 to benefit from the fruits of his /her hard work.

Odds for ICC World Cup Win

I found the following at this site : http://www.cricket-worldcup.net/finals.html

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India v Sri Lanka Win Betting - 02/04/11

• Sri Lanka v India - 02/03/11

India are 4/6 to win, Sri Lanka are 6/5 to win with Boylesports

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If converted to probability this means that probability of India winning is 0.4 and that for Sri Lanka winning is 0.545. It is interesting to observe that these two probabilities do not add up to 1.

Suppose now the betting house sells one bet of $100 for India winning to A and another bet of $100 on Sri Lanka winning to B.

Then in case India wins the betting house returns $100 (to A) and pays out $150 additional (to A). It keeps $100 of B. So the net loss for the house is $50.

In case SriLanka wins the betting house returns $100 (to B) and pays out $83.33 (to B). It keeps $100 of A. So the net gain for the house is $16.77

How is the betting house going to make money then? The answer possibly is that it expects lot more gamblers to bet on Sri Lanka winning than on India winning. This can be explained from prospect theory. Since, the chance of Sri Lanka winning is more than that of India winning, for a gambler the chance of losing $100 is more when betting for India than for Sri Lanka. This will drive a larger number of gamblers to bet for Sri Lanka. The fact that they (gamblers) stand to gain about 80% more if they win by betting for India than for Sri Lanka is likely to be overridden by the fact that the chance of losing of $100 is 32% more when betting for India than for Sri Lanka.

An interesting illustration of Prospect Theory is practice !!!

Will Sensex hit 21000 before Diwali?

I saw a news item in a newspaper website speculating that the Sensex will cross 21000 prior to Diwali. As per my calculations the chance is not that bright. It is only about 9%.

Here is the probability distribution of the value of Sensex on the pre-Diwali day:

Less than 19000 - 5%

Between 19000 to 19500 - 14%

Between 19500 - 20000 - 28%

Between 20000 - 20500 - 26%

Between 20500 - 21000 - 18%

Above 21000 - 9%

Happy Diwali!

Octopus Paul - Psychic Forecaster

It is amazing to see how chance can fool us!!! Look at the worldwide craze about octopus Paul. The eight legged creature got six successive predictions about Germany's games correct and is being heralded as a "psychic forecaster". Nobody (especially the journalists) seems to be asking the simple question - How often will that happen just at random? The answer is also easy to compute. The Octopus's prediction can be thought of as a string of heads and tails obtained from tosses of a fair coin. The probability that the string generated by the octopus matches the actual string is

= (1/ 2^6)= 1/64 = 0.015. That is the chance is about 1.5%. What we have seen is an occurrence of a low probability event and we are immediately driven to see a pattern!!! Fooled by Randomness!

How low can Sensex go this month?

The sudden fall in the BSE-Sensex has disturbed many a investor and the question foremost in their mind is: How low can this get? I try to answer this question quantitatively below.

Here are my predictions for the lowest value of Sensex for the period 4-Nov to 30-Nov.

Chance of Sensex closing below 15000 on someday within this period: 58%

Chance of Sensex closing below 14000 on someday within this period: 14%

Chance of Sensex closing below 13000 on someday within this period: 2%

Another question that investors are interested in are the chances of an upswing. The chances of these positive happenings are given below:

Chance of Sensex closing above 16000 on someday within this period: 55%

Chance of Sensex closing above 17000 on someday within this period: 17%

Chance of Sensex closing above 18000 on someday within this period: 4%

On NIFTY-2

Here are my predictions of the possible closing value of NIFTY for the next week:

Date P5 Q1 Med Q3 P95

5-Oct 4921 5042 5089 5136 5226

6-Oct 4870 5015 5093 5165 5291

7-Oct 4830 5003 5099 5190 5341

8-Oct 4795 4990 5104 5216 5394

9-Oct 4772 4980 5111 5234 5438

P5 = 5th percentile

Q1 = 25th percentile

Med = 50th percentile

Q3 = 75th percentile

P95 = 95th percentile