Lecture No.2 By M Fahad Siddiqi Lecturer- Finance

Menu for todays Lecturer O Review of Return calculations O Difference Between AM returns and GM returns. O What is Moving Averages Returns, Types and Uses. O What is Variance and Standard deviation. O What is risk ? Different types of Risk.

10-3 Arithmetic vs. Geometric Mean O Arithmetic average: O Return earned in an average period over multiple periods O Answers the question: “What was your return in an average year over a particular period?” O Geometric average: O Average compound return per period over multiple periods O Answers the question: “What was your average compound return per year over a particular period?” O Geometric average < arithmetic average unless all the returns are equal

10-4 Geometric Average Return: Formula Where: R i = return in each period T = number of periods

10-5 Geometric Average Return Where: Π = Product (like Σ for sum) T = Number of periods in sample R i = Actual return in each period

10-6 Example: Calculating a Geometric Average Return Example 10.4

10-7 Arithmetic vs. Geometric Mean Which is better? O The arithmetic average is overly optimistic for long horizons O The geometric average is overly pessimistic for short horizons O Depends on the planning period under consideration 15 – 20 years or less: use arithmetic 20 – 40 years or so: split the difference between them 40 + years: use the geometric

Moving Average Basics O One of the techniques many analysts use in judging internal relative strength involves the creation of moving averages of prices. A moving average is one of the simplest trend-following tools investors use. While moving averages come in different flavors, their underlying purpose remains the same: to help investors and traders track the trend in the prices of financial assets by smoothing out the periodic fluctuations in price (also called “noise”).

Moving Average Basics O Types of Moving Averages O Simple Moving Average O Weighted Moving Average O Exponential Moving Average

Simple Moving Average O A simple moving average, or SMA, applies equal weights to all prices across the time interval used to calculate the average. As a result, a simple moving average assumes that prices from the beginning of the period are just as relevant as prices from the end of the period. O (P1+ P2+ P3+ … + Pn) ÷ n O Where:P1= the price of the first period used to calculate the moving Average O Pn= is the price of the last period used to calculate the moving average O n = the number of periods used in calculating the moving average

Weighted Moving Average O A weighted moving average (WMA) explicitly assigns weights that determine the relative importance of the prices used. While higher weights are usually assigned to the most recent prices, you can use any scheme you wish. O ((n × Pn) + ((n – 1) × Pn-1) +((n – 2) × Pn-2) + … ((n – (n – 1))× Pn – (n – 1)) ÷ (n + (n – 1) + (n – 2) + … + (n – (n – 1))) O Where: O n = the number of periods used in calculating the moving average O Pn= the price of the most recent O period used to calculate

Exponential Moving Average O Like the weighted moving average, the exponential moving average (EMA) reduces the lag by giving more emphasis to recent prices. Also like the weighted moving average, the weighting applied to the most recent price depends on the number of periods in the moving average. These weighting factors decrease exponentially, giving much more importance to recent prices, while still not discarding older observations entirely.

Exponential Moving Average O There are three steps to calculating an exponential moving average: O 1. Calculate the weighting multiplier; O 2. Derive the initial “EMA,” which can be a simple moving average of previous values or the price value of the previous period; O 3. Calculate the exponential moving average. O Here are the equations: O Multiplier= (2÷ (n+1)) O EMA =[Close–EMA(previousday)] × O multiplier+EMA(previousday) O Lets work out Lets work out

Return Variability: The Second Lesson Variance A common measure of volatility. Standard deviation The square root of the variance. Normal distribution A symmetric bell-shaped frequency distribution that is completely defined by its average and standard deviation.

Return Variability: Variance of return where N is the number of returns Standard deviation of return

Expected Return O measuring likely future return O based on probability distribution O random variable E(R) =SUM(R i x Prob(R i ))

example 1 RProb(R) 10%.2 5%.4 -5%.4 E(R) =(.2)10% + (.4)5% + (.4)(-5%) = 2%

example 2 RProb(R) 1%.3 2%.4 3%.3 E(R) =(.3)1% + (.4)2% + (.3)(3%) = 2%

examples 1 & 2 O same expected return O but not same return structure O returns in example 1 are more variable

Risk O measure likely fluctuation in return O how much will R vary from E(R) O how likely is actual R to vary from E(R) O measured by O variance (    O standard deviation 

  = SUM[(R i - E(R)) 2 x Prob(R i )]  SQRT(  

example 1   = (.2)(10%-2%) 2 = (.4)(5%-2%) 2 + (.4)(-5%-2%) 2  = 6.24%

example 2   = (.3)(1%-2%) 2 = (.4)(2%-2%) 2 + (.3)(3%-2%) 2  =.77%

O same expected return O but example 2 has a lower risk O preferred by risk averse investors O variance works best with symmetric distributions So we Can Conclude

symmetricasymmetric E(R) R PROB(R) R E(R)

Risk Premium and Fundamental Risk O Business risk O Financial risk O Liquidity risk O Exchange rate risk O Country risk

Business Risk O Uncertainty of income flows caused by the nature of a firm’s business affect income flows to an investor. O Investors demand a risk premium based on the uncertainty caused by the basic business of the firm.

Financial Risk O Uncertainty is introduced by the method by which the firm finances its investments. O Borrowing requires fixed payments which must be paid ahead of payments to stockholders. O The use of debt increases uncertainty of stockholder income and causes an increase in the stock’s risk premium.

Liquidity Risk O Uncertainty is introduced by the secondary market for an investment. O How long will it take to convert an investment into cash? O How certain is the price that will be received? O Investors increase their required rate of return to compensate for liquidity risk.

Exchange Rate Risk O Uncertainty of return is introduced by acquiring securities denominated in a currency different from your own. O Changes in exchange rates affect the investors return when converting an investment back into the “home” currency.

Country Risk O Political risk is the uncertainty of returns caused by the possibility of a major change in the political or economic environment in a country. O Individuals who invest in countries that have unstable political-economic systems must include a country risk- premium when determining their required rate of return.

Total Risk Risk Premium is a function of O Business Risk, O Financial Risk O Liquidity Risk O Exchange Rate Risk O Country Risk

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