For every rupee I earn, I pay 30 paise as tax (30%). When I take that 70 paise to a retaurant, I can only buy stuff worth 50.4 paise as I have to pay 20% VAT and 10% service charges.
So that means that the can of Guinness that I thought was 350 bucks actually cost me 700 bucks of my earned salary!!!
What happens when you eat a cherry on top of somebody else’s ice cream and then casually remark: “I took your cherry”.
To get a dead tree comic I am doing this. As you can see, I really really want it.
A friend of me asked these 5 questions long long ago...
1. During the past few months, major league baseball players were in the process of negotiating with the team owners for higher minimum salaries and more fringe benefits. At the time of the negotiations, most of the major league baseball players had salaries in the $100,000 - $150,000 a year range. However, there were a handful of players who, via the free agent system, earned nearly three million dollars per year. Describe the advantages and disadvantages of the median and mean in describing the 'average' salary.
The handful of players are outliers. The best approach for this analysis would be finding mean, standard deviation and skewness of data. Mean and standard deviation should be found out ignoring the outliers and skewness should be visualised using curve projection. Curve projection can be done with or without the outliers. However the gradient and the main projection area should not be compromised to include outliers.
Mean : Mean is simply the average of the data. The handful of outliers would distort the mean. However this would also depend on the numbers of players in the given range, In case the outliers are less than .5%, mean can be assumed to reasonably represent the given data. However mean as a standalone figure should not be used. Using standard deviation with mean would give us a reasonable estimate of the data.
Median : Median is the middlemost value of a population. In case of this data, median would be reasonable figure if the population was more than 1000. Then the median would ignore the outliers without moving away from the middle of distribution. Median would be useful here when viewed with mode of the frequency for small ranges within the given range.
No. As much my friends might have downplayed her nuisances, I would have got sense knocked into my head somehow. It might have taken some more time though.
No. As I went further in my Actuarial exams, comparing Assets and Liabilities took the top priority. Now I compare them for a long future term. Sometimes 100 years.
4. Which Hindi Movie comedian do you most identify with?
IS Johar. That deadpan humor is me.
5. Name one person/thing you love with so much passion, it actually hurts.
My Actuarial exam pass certificates. Try touching them sometime, it'll actually hurt :)
Brilliant editorial in this month’s The Actuary magazine.
Get real with equations
There is a disturbing new force at work in our society. More insidious than heroin or those pirate Finding Nemo DVDs which directly fund global terrorism, it threatens to strike at everything we hold dear.
Rogue equations are on the loose.
They began innocently a couple of years ago. Quirky Christmas articles in the Sun on the area of wrapping paper required for a Toblerone and suchlike, but they were one-offs written by desperate professors to feed their starving children and make their Christmas a little less miserable.
But now the malaise seems to be spreading. Recent issues of Cosmopolitan, with formulae for the perfect relationship, the perfect boyfriend, and the perfect career, have contained more maths than The Actuary. That can’t be right. And I have a sneaking suspicion that very little of it is properly peer-reviewed. Or even makes sense.
Digging a little deeper I turned up a seedy little underworld of backstreet academics trading equations for cash. In the old days, if you were a biscuit company wanting to get your name in the tabloids you had to go to the trouble of commissioning a bogus survey on the nation’s dunking habits. But now you can slip a mathematician a few bob and he’ll scribble down some algebra to find the perfect dunking angle before zipping off in his Lamborghini with a supermodel in the passenger seat. Pow! – instant headline. Of course, the maths doesn’t actually have to make sense. Who’s going to notice?
Dr Cliff Arnall, a health psychologist at Cardiff University, could lay a claim to being the Heidi Fleiss of this secret world. Already this year he has helped firms to find the formulae for the happiest day of the year and the best day to make a resolution. His latest offering is the formula for the perfect long weekend:
(C x R x ZZ)/((Tt + D) x St) + (P x Pr) >400
Tt = travel time
D = delays
C = time spent on cultural activities
R = time spent relaxing
ZZ = time spent sleeping
St = time spent in a state of stress
P = time spent packing
Pr = time spent in preparation
This is not good maths. For starters, what time units are used? Presumably they are needed to make sense of the threshold of 400 required for a fun time. It is also nonsense dimensionally, with mixed dimensions of T and T2 on the left-hand side. Finally, it implies that an infinitely good time can be had by staying at home and cutting your travel time to zero. Dr Arnall clearly enjoys packing though – perhaps he is a proper mathematician after all.
In the meantime, I am pleased to announce the founding of the Campaign for Real Equations. CAMRE will be a haven for like-minded individuals to grow beards, wear sandals, and extol the virtues of old-fashioned equations, identities, and functions. There will also be an annual CAMRE guide, listing places where one can be assured of equations of utmost quality, which will definitely feature The Actuary. And possibly Cosmopolitan, if it finally manages to come up with a proper formula for the perfect girl’s night in.
_ TRISTAN WALKER-BUCKTON
If you come to this page and wonder why I don't update my blog, here is the reason :
On completion of this subject the trainee actuary will be able to:
(i) Discuss the advantages and disadvantages of different measures of investment risk.
1. Define the following measures of investment risk:
variance of return
downside semi-variance of return
Value at Risk (VaR) / Tail VaR
2. Describe how the risk measures listed in (i) 1. above are related to the form of an investor's utility function.
3. Perform calculations using the risk measures listed above to compare investment opportunities.
4. Explain how the distribution of returns and the thickness of tails will influence the assessment of risk.
(ii) Describe and discuss the assumptions of mean-variance portfolio theory and its principal results.
1. Describe and discuss the assumptions of mean-variance portfolio theory.
2. Discuss the conditions under which application of mean-variance portfolio theory leads to the selection of an optimum portfolio.
3. Calculate the expected return and risk of a portfolio of many risky assets, given the expected return, variance and covariance of returns of the individual assets, using mean-variance portfolio theory.
4. Explain the benefits of diversification using mean-variance portfolio theory.
5. Explain what is meant by: opportunity set, efficient frontier, indifference curves and the optimum portfolio, in the context of mean-variance portfolio theory.
(iii) Describe and discuss the properties of single and multifactor models of asset returns.
1. Describe the three types of multifactor models of asset returns:
fundamental factor models
statistical factor models
2. Discuss the single index model of asset returns.
3. Discuss the concepts of diversifiable and non-diversifiable risk.
4. Discuss the construction of the different types of multifactor models.
5. Perform calculations using both single and multi-factor models
(iv) Describe asset pricing models, discussing the principal results and assumptions and limitations of such models.
1. Describe the assumptions and the principal results of the Sharpe-Lintner-Mossin Capital Asset Pricing Model (CAPM).
2. Discuss the limitations of the basic CAPM and some of the attempts that have been made to develop the theory to overcome these limitations.
3. Discuss the assumptions, principal results and limitations of the Ross Arbitrage Pricing Theory model (APT).
4. Perform calculations using the CAPM.
(v) Discuss the various forms of the Efficient Markets Hypothesis and discuss the evidence for and against the hypothesis.
1. Discuss the three forms of the Efficient Markets Hypothesis and their consequences for investment management.
2. Describe briefly the evidence for or against each form of the Efficient Markets Hypothesis.
(vi) Demonstrate a knowledge and understanding of stochastic models of the behaviour of security prices.
1. Discuss the continuous time log-normal model of security prices and the empirical evidence for or against the model.
2. Discuss the structure of auto-regressive models of security prices and other economic variables, such as the Wilkie model, and describe the economic justification for such models.
3. Discuss the main alternatives to the models covered in (vi) 1. and (vi) 2. above and describe their strengths and weaknesses.
4. Perform simple calculations involving the models described above.
5. Discuss the main issues involved in estimating parameters for asset pricing models:
stationarity of underlying time series
the role of economic judgement
(vii) Define and apply the main concepts of Brownian motion (or Wiener Processes).
1. Explain the definition and basic properties of standard Brownian motion or Wiener process.
2. Demonstrate a basic understanding of stochastic differential equations, the Ito integral, diffusion and nean-reverting processes.
3. State Ito s formula and be able to apply it to simple problems.
4. Write down the stochastic differential equation for geometric Brownian motion and show how to find its solution.
5. Write down the stochastic differential equation for the Ornstein-Uhlenbeck process and show how to find its solution.
(viii) Demonstrate a knowledge and understanding of the properties of option prices, valuation methods and hedging techniques.
1. State what is meant by arbitrage and a complete market.
2. Outline the factors that affect option prices.
3. Derive specific results for options which are not model dependent:
Show how to value a forward contract.
Develop upper and lower bounds for European and American call and put options.
Explain what is meant by put-call parity.
4. Show how to use binomial trees and lattices in valuing options and solve simple examples.
5. Derive the risk-neutral pricing measure for a binomial lattice and describe the riskneutral pricing approach to the pricing of equity options.
6. Explain the difference between the real-world measure and the risk-neutral measure. Explain why the risk-neutral pricing approach is seen as a computational tool (rather than a realistic representation of price dynamics in the real world).
7. State the alternative names for the risk-neutral and state-price deflator approaches to pricing.
8. Demonstrate an understanding of the Black-Scholes derivative-pricing model:
Explain what is meant by a complete market.
Explain what is meant by risk-neutral pricing and the equivalent martingale measure.
Derive the Black-Scholes partial differential equation both in its basic and Garman- Kohlhagen forms.
Demonstrate how to price and hedge a simple derivative contract using the martingale approach.
9. Show how to use the Black-Scholes model in valuing options and solve simple examples.
10. Discuss the validity of the assumptions underlying the Black-Scholes model.
11. Describe and apply in simple models, including the binomial model and the Black-Scholes model, the approach to pricing using deflators and demonstrate its equivalence to the risk-neutral pricing approach.
12. Demonstrate an awareness of the commonly used terminology for the first, and where appropriate second, partial derivatives (the Greeks) of an option price.
13. Describe how the Greeks are used in the risk management of a portfolio of derivatives.
14. Derive the partial derivatives described above for Black-Scholes European option prices and describe their general characteristics.
15. Demonstrate an understanding of the concept of delta-hedging and show how to apply it.
(ix) Demonstrate a knowledge and understanding of models of the term structure of interest rates.
1. Describe the desirable characteristics of a model for the term-structure of interest rates.
2. Describe, as a computational tool, the risk-neutral approach to the pricing of zerocoupon bonds and interest-rate derivatives for a general one-factor diffusion model for the risk-free rate of interest.
3. Describe, as a computational tool, the approach using state-price deflators to the pricing of zero-coupon bonds and interest-rate derivatives for a general one-factor diffusion model for the risk-free rate of interest.
4. Demonstrate an awareness of the Vasicek, Cox-Ingersoll-Ross and Hull-White models for the term-structure of interest rates.
5. Discuss the limitations of these one-factor models and show an awareness of how these issues can be addressed.
End of Syllabus
End Result : 34 students appeared and 4 passed. Your grade was FA (1% to 5% below passing marks).
Yeah, I know. Shit Happens!!!
An Excellent Article published in this month's The Actuary magazine.
Batting on a statisticky wicket</font>Jurie Nel puts forward a classification scheme for the consistency of cricket batsmen.
When a cricketer goes out to bat, his career statistics are shown on the television screen. The most important figure quoted is his average score, but nothing is indicated about his consistency. This information, however, should be of considerable interest to the viewer. In this article I shall explain why.
The lazy guy has got up and prepared a quiz.
Check it out here