Cheat Sheet Quantitative Methods

Question 1

Arithmetic, geometric and harmonic mean returns

Answer 1

Arithmetic Mean > Geometric Mean > Harmonic Mean

(Geometric Mean)2 = Arithmetic Mean x Harmonic Mean

Question 2

Normal distribution

Answer 2

• 68% of observations lie in between μ +/- 1σ;
• 90% of observations lie in between μ +/- 1.65σ;
• 95% of observations lie in between μ +/- 1.96σ;
• 99% of observations lie in between μ +/- 2.58σ;

Question 3

The properties of lognormal distributions are:

Answer 3

• It cannot be negative
• The upper end of its range extends to infinity
• It is positively skewed.

For these reasons, lognormal distribution is suitable for model asset prices, not asset returns (since returns can be negative).

If X follows a lognormal distribution, then ln(X) follows a normal distribution.

Question 4

Central Limit Theorem

Answer 4

Der Zentrale Grenzwertsatz besagt, dass der Durchschnitt (oder die Summe) von vielen zufälligen Werten, egal wie diese ursprünglich verteilt sind, näherungsweise eine Glockenkurve (Normalverteilung) bildet, wenn genug Werte betrachtet werden.

Das bedeutet: Wenn du oft genug eine Stichprobe ziehst und die Mittelwerte anschaust, werden diese immer mehr einer Normalverteilung ähneln – egal, wie die Daten ursprünglich verteilt waren.

Question 5

Assumptions of simple linear regression

Answer 5

• Linear relationship between X and Y
• Homoscedasticity (constant variance of residuals for all observations)
• Independence between X and Y (residuals are uncorrelated for all observations)
• Normality of the residuals