# Fight Finance

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 Portfolio Details Stock Expected return Standard deviation Covariance $(\sigma_{A,B})$ Beta Dollars invested A 0.2 0.4 0.12 0.5 40 B 0.3 0.8 1.5 80

What is the standard deviation (not variance) of the above portfolio? Note that the stocks' covariance is given, not correlation.

 Portfolio Details Stock Expected return Standard deviation Correlation $(\rho_{A,B})$ Dollars invested A 0.1 0.4 0.5 60 B 0.2 0.6 140

What is the standard deviation (not variance) of the above portfolio?

Find the sample standard deviation of returns using the data in the table:

 Stock Returns Year Return pa 2008 0.3 2009 0.02 2010 -0.2 2011 0.4

The returns above and standard deviations below are given in decimal form.

Let the standard deviation of returns for a share per month be $\sigma_\text{monthly}$.

What is the formula for the standard deviation of the share's returns per year $(\sigma_\text{yearly})$?

Assume that returns are independently and identically distributed (iid) so they have zero auto correlation, meaning that if the return was higher than average today, it does not indicate that the return tomorrow will be higher or lower than average.

A stock's standard deviation of returns is expected to be:

• 0.09 per month for the first 5 months;
• 0.14 per month for the next 7 months.

What is the expected standard deviation of the stock per year $(\sigma_\text{annual})$?

Assume that returns are independently and identically distributed (iid) and therefore have zero auto-correlation.

An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 12% pa.

• Stock A has an expected return of 10% pa and a standard deviation of 20% pa.
• Stock B has an expected return of 15% pa and a standard deviation of 30% pa.

The correlation coefficient between stock A and B's expected returns is 70%.

What will be the annual standard deviation of the portfolio with this 12% pa target return?

Which of the following statements about standard statistical mathematics notation is NOT correct?

The standard deviation and variance of a stock's annual returns are calculated over a number of years. The units of the returns are percent per annum $(\% pa)$.

What are the units of the standard deviation $(\sigma)$ and variance $(\sigma^2)$ of returns respectively?

Hint: Visit Wikipedia to understand the difference between percentage points $(\text{pp})$ and percent $(\%)$.

Which of the following statements about an option (either a call or put) and its underlying stock is NOT correct?

Which of the following statements about an option (either a call or put) and its underlying stock is NOT correct?

 European Call Option on a non-dividend paying stock Description Symbol Quantity Spot price ($) $S_0$ 20 Strike price ($) $K_T$ 18 Risk free cont. comp. rate (pa) $r$ 0.05 Standard deviation of the stock's cont. comp. returns (pa) $\sigma$ 0.3 Option maturity (years) $T$ 1 Call option price ($) $c_0$ 3.939488 Delta $\Delta = N[d_1]$ 0.747891 $N[d_2]$ $N[d_2]$ 0.643514 Gamma $\Gamma$ 0.053199 Theta ($/year) $\Theta = \partial c / \partial T$ 1.566433

Which of the following statements about an asset’s standard deviation of returns is NOT correct? All other things remaining equal, the higher the asset’s standard deviation of returns: