• Efficient market hypothesis is subject to interpretation

The formulation on Investopedia seems to me the best:

The efficient market hypothesis (EMH) is an investment theory that states it is impossible to “beat […]

• The Newey-West estimator: uncorrelated and correlated data

I hate long posts but here we by necessity have to go through all ideas and calculations, to understand what is going on. One page of formulas in A. […]

• Different faces of vector variance: again visualization helps

In the previous post we defined variance of a column vector \$latex X\$ with \$latex n\$ components by

\$latex V(X)=E(X-EX)(X-EX)^T.\$

In terms of […]

• Variance of a vector: motivation and visualization

I always show my students the definition of the variance of a vector, and they usually don’t pay attention. You need to know what it is, already at the level o […]

• Solution to Question 2 from UoL exam 2016, Zone A (FN3142)

This is another difficult question, and I don’t think it will appear again in its entirety. However, the ideas applied here and here are worth repeating […]

• Law of total probability – you could have invented this

A knight wants to kill (event \$latex K\$) a dragon. There are two ways to do this: by fighting (event \$latex F\$) the dragon or by outwitting (\$latex O\$) it. […]

• Sampling from uniform distribution – example of convolution

For the intuition behind the uniform distribution see this post. More formally, let us fix an interval \$latex [a,b]\$. We say that a random […]

• Density of a sum of independent variables is given by convolution

This topic is pretty complex because it involves properties of integrals that economists usually don’t study. I provide this result to be able to […]

• Solution to Question 1 from UoL exam 2017, Zone B (FN3142)

This is a relatively simple problem but surprisingly many students cannot answer it. I provide two answers, the first of which gives a general idea about […]

• Solution to Question 1 from UoL exam 2016, Zone B

This problem is a good preparation for Question 2 from UoL exam 2015, Zone A (FN3142), which is more difficult.

Problem statement

Two corporations each have a […]

• Solution to Question 1 from UoL exam 2016, Zone A  (FN3142)

Frankly, this is a crazy exercise. I deserve full 100 marks for this solution but I wouldn’t be able to solve this during an exam. In the problem s […]

• Expected shortfall is next after Value at Risk

A few years ago I took my American friend to Astana. It was the beginning of March, not the coldest time of the year, but it was impossible to walk in the street for […]

• Conditional expectation generalized to continuous random variables

The conditional expectation definition needs to be generalized, to be applicable to continuous random variables. The generalization is […]

• Value at Risk and its calculation for a normal distribution

Variance is a symmetric measure of risk. Positive and negative values of the measured variable equally influence variance. Value at Risk is an […]

• From minimum to infimum: Math is just a logical game

The true Math is a continuous exercise in logic. A good teacher makes that logic visible and tangible. A genius teacher does the logic mentally and only […]

• Distribution function estimation

The relativity theory says that what initially looks absolutely difficult, on closer examination turns out to be relatively simple. Here is one such topic. We start with a […]

• See if this definition of a function is better than others

Try the definitions from the Khan Academy, Math is Fun, Wikipedia, Paul’s Online Math Notes, and there are some others. Most of them are obsessed with […]

• Visualization of payoffs on calls and puts

Earlier I provided the traditional view of the call option value. In this post I give an alternative, more visual representation of the payoff on calls and puts, both […]

• Logical structure of definitions

Roughly speaking, there are two types of Math: formula Math, where all calculations can be seen, and abstract (or invisible) Math, which happens in the head. In my Optimization […]

• Intro to option greeks: theta, intrinsic value and time value

This world is full of surprises and uncertainties. One thing is for sure: time is unidirectional and nobody grows younger. This is true also for […]