Normal Distribution and Stock markets

 You toss a coin , 100 times, what is the number of heads you expect? 500 employees of a company, appear for a test(multiple choice Qs with 1 right ans out of 4 choices) having 100 questions. Employees attend without preparation and have no clues on the subject (say quantum mechanics). How many will get 100/100? How many will get zero?

Can we connect the results with stock markets? We pick up 100 stocks randomly and construct a portfolio. What would be the returns after 20 years?

 First 2 events are random events. Probability theory suggests, the results of the first two will follow normal distribution if we do experiment for a large number of times. What normal distribution curve says? You can expect a value clustered around the mean(=no of experiments* probability of success). Most of the times you would end getting 45-55 heads if you toss a coin for 100 times. Getting 100 heads/tails are extremely rare, Even 80 heads will be quite rare event.

 Similarly, many people would get around 25 marks. Most of the people would score between 16-34 marks. Number of people getting 50 and above would be quite less.

 Eugene Fama, Robert Shiller along with Peter Hansen shared Nobel prize for economics in 2013. Fama’s works revolves around efficient market, which says that capital market prices in, all the information quite quickly. So all stock prices are always rightly priced. For example, if a company like Infosys comes with stellar results during  market hours, within seconds, it’s stock price will go up. This news and possible improved prospects would be priced in fast. You cannot make easy money. The future price will be determined by the future news flows which could be positive or negative, which are random in nature.

 To model stock prices in such situation, random walk model can be used. The returns of a stock goes up by say, 1 percent, say if the coin turns head(good news). It goes down by say ½ percent if it’s a tail. The stock returns in such cases will follow normal distribution over long period. This could be the reason some risk/return /pricing model assume Normal distribution for the underlying asset.( In real world, perfect normal distribution cannot explain wild swings resulted by black swan events. So daily returns has fatter tails than ND. Ref Fama)

Robert Shiller, a behavioural economics proponent, believes markets are not always efficient. There could be bubbles. Over a long period it could be predictable. He has successfully predicted dotcom, housing bubbles and off late, gold bubble.

 

Comments

Post a Comment

Popular posts from this blog

5:Continuous compounding formulas and Euler's number

Let see compounding interest formulas.  If P is principal r is interest rate per annum (for 10% interest, r = 0.1)   interest for one year = principal *interest rate = P*r . Total amount after one year =Principal + interest =P+Pr. In annually compound interest rate regime P+Pr = P(1+r) become principal at the end of first year.  Then the next year interest would be calculated on this principal P(1+r) r would be interest for the second year. At the end of second year, total amount would be = P(1+r)+P(1+r) * r = P(1+r)^2 After n years total amount = P(1+r)^n For the same interest rate r, after 6 months how much interest would have been accumulated? Half of the annual interest , that is Pr/2    If interest is compounded to principal semi-annually, at the end of first 6 months Total amont= P+Pr/2=P(1+r/2). For the next 6 months interest will be calculated on this. Interest =P(1+r/2)* r/2. Total amount at the end of one year =P(1+r/2) +(P(1+
Read more

3-Jackson Hole 2005

United states of America has political and economic influence all over the world.With 33  crore people out of 759 cr world population(around 5%) its GDP is more than 20% of worlds GDP(Nominal not PPP). US Defence budget a year is almost equal to all other countries defence budgets put together. US spending on health care is more than India's annual GDP. In a Nation's economic well-being  two things play important role. Fiscal policy, Govt decides, deals with how Govt gets its money and spends. Second one is monetary policy, controlled by central bankers.Given the size of economy , policies in US not only affect US, but rest of the world as well, in the globalised world. Federal reserve which controls the monetary policy in US.Alan Greenspan was Fed Chairman for 18 years in US . A raise in interest rate, or a cut, could not only affect US but the entire worlds economy. During Clinton regime , US economy had a robust growth. When there is a good growth, the unemployment rate
Read more

Yield curve and sensitivity

  If you assume there is no default risk, fixed coupon bonds pay fixed ( predictable) cashflows throughout its lifetime. That doesn’t mean it is risk-free. You can make capital gain or loss on fixed coupon bonds depending on the prevailing market rate. Quantifying it, can help in risk mitigation. For example in US rate is expected to go up in future and in India it is widely expected that rate needs to come down. This will have impact on all bond prices. In such cases, we need to know how the yield changes of a bond affects its prices.   Assume a coupon with 100 face value , with 10% annual coupon rate for 10 years. For simplicity, On day one , let’s assume interest rate is so volatile and it can vary between 0-24% rather than staying at 10%. What will be the bond price at each yield? We can use yield to maturity equation below to calculate bond prices at each yield and we can plot it in a diagram( java program attached. Raname priceyield.txt to jar and double click to launch if you ha
Read more