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CHAPTER 30

Trading portfolios are not totally free of risk. The volatility of a market variable measures

uncertainty about the future value of the variable. It is important for risk managers to monitor thevolatilities of market variables in order to assess potential losses.

3.1 DEFINITION OF VOLATILITY

Volatility is a measure ofdispersion around the mean or average return of a security. One way to

measure volatility is by using the standard deviation, which tells you how tightly the price of a

stock is grouped around the mean ormoving average (MA). When the prices are tightly bunched

together, the standard deviation is small. When the price is spread apart, you have a relatively

large standard deviation.

For securities, the higher the standard deviation, the greater the dispersion of returns and the

higher the risk associated with the investment. As described bymodern portfolio theory (MPT),

volatility creates risk that is associated with the degree of dispersion of returns around the

average. In other word, the greater the chances of lower-than-expected return, the riskier the

investment is.

The volatility of a variable is defined as the standard deviation of the return provided by the

variable per unit of time when the return is expressed using continuous compounding. When

volatility is used for option pricing, the unit of time is usually one year, so that volatility is the

standard deviation of the continuously compounded return per year.

is equal to the standard deviation of in (St/So), where St is the value of the market variable at

time T and So is its value today. The expression In (St/So) equals the total return (not the return

per unit time) earned in time T expressed with continuous compounding. If is per day, T is

measured in days, if is per year, T is measured in year.

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3.2 MARKET PERFORMANCE AND VOLATILITY

There is a strong relationship between volatility and market performance. Volatility tends to

decline as the stock market rises and increase as the stock market falls. When volatility increases,

risk increases and returns decrease. Risk is represented by the dispersion of returns around mean.

The greater the dispersion of returns around the mean, the larger is the drop in thecompound

return.

3.3ESTIMATING VOLATILITY FROM HISTORICAL DATA

When the volatility of a variable is estimated using historical data, it is usually observed at fixed

intervals of time (e.g., every day, week, or month). Define:

N+1: Number of observations

: Value of variable at end of interval, where _ =0, 1,, n

: Length of time interval.

And let

=

For i = 1, 2, . . . , n

The usual estimate s of the standard deviation of the Ui is given by

S =

Where is the mean of the

The standard deviation of the Ui is where the volatility of the variable is. The variable s is,

therefore, an estimate of . It follows that it self can be estimated as where The standard

error of this estimate can be shown to be approximately . If is measured in years, the

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volatility that is calculated is a daily volatility. we can now illustrate the average return and

yearly volatility of 25 CSE listed companies as follows:

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Sectors Company Averagereturn

Dailyvolatility

(%)

Yearlyvolatility

(%)

InsuranceGREEN DELTAINSURANCE

0.003842 3.92 62.23

PRAGATIINSURANCE

0.002401 4.04 64.13

Textiles and clothing SQUARETEXTILES LTD

0.000319 2.15 34.13

Pharma and chemicalSQUARE

PHARMACEUTICALS LTD

0.000551 3.15 50

cementHEIDELBERG

CEMENT BD LTD0.001443 2.56 40.64

MEGHNA CEMENTMILLS LTD

0.001205 3.86 61.28

Engineering and

electrical

AFTAB

AUTOMOBILESLTD

0.00294 3.81 50.48

Leather and footwearAPEX ADELCHI

FOOTWARE LTD0.003029 5.05 80

BATA SHOECOMPANY BD LTD

0.001866 2.99 47.46

EnergyBOC BD LTD 0.001734 3.09 49.05

PADMA OILCOMPANY LTD

0.000108 4.77 75.72

Bank

AB BANK LTD -0.00077 5.52 87.63

NATIONAL BANKLTD

-0.0011 4.04 64.13

UTTARA BANKLTD

-0.00046 4.05 64.29

IFIC BANK -0.00106 4.99 79.21

SOUTHEASTBANK LTD

-0.00021 2.23 35.4

EXIM BANK BDLTD

-0.00038 1.98 31.43

NCC BANK LTD 0.00023 2.42 38.42

ISLAMI BANK BD

LTD

0.000443 2.42 38.42

ICT BANGLADESHONLINE LTD

0.000972 3.84 60.96

Leasing & financingIDLC FINANCE

LTD0.001402 3.79 60.16

UTTARA FINANCE& INVESTMENT

LTD

0.000745 2.7 42.86

Miscellaneous

USMANIA GLASSSHEET FAC LTD

0.001986 3.74 59.37

GQ BALL PENINDUSTRIES LTD

0.002626 4.1 65.06

ARAMIT LIMITED 0.003407 5.04 80

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TABLE: the volatility of 25 listed companies of CSE for 5 years from 2005 to 2009.

From the above table we can see that the banking sector in the stock market experienced much

volatile price compare to other listed companies of CSE. AB bank has highest yearly volatility of87.63% where EXIM bank has the lowest yearly volatility of 31.43% and other stayed in the

range of 30% to 79%, where all the banks except NCC bank has negative return. Moreover from

the sector of leather and footwear APEX ADELCHI FOOTWEAR LTD has 80% of yearly pricevolatility as same of ARAMIT LTD. The yearly volatility in insurance sector lies between 62% -

65%. Huge difference can be seen in energy sector where the yearly volatility differ 25 %( app)

between two company.

Stocks and the Beta Coefficient

The Beta Coefficient is a means of measuring the volatility of a security or ofan investing portfolio of securities in comparison with the market as a whole.

In other words, Beta is the sensitivity of a stock's returns to the returns onsome market index.

Beta is calculated using regression analysis. A Beta of 1 indicates that the

security's price will move with the market. A Beta greater than 1 indicatesthat the security's price will be more volatile than the market and finally, a

Beta less than 1 means that it will be less volatile than the market.

Beta values can be characterized as follows:

b Less than 0:

Negative Beta is possible but not likely. People thought gold stocks should

have negative Betas but that hasn't been true.

b Equal to 0:

Cash under your mattress, assuming no inflation!

Beta Between 0 and 1:

Low-volatility investments (e.g., utility stocks).

b Equal to 1:

Matching the index.

b Greater than 1:

http://www.greekshares.com/index-6.phphttp://www.greekshares.com/index-6.php

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It means anything is more volatile than the index.

b Much Greater than 1:

It is Impossible, because the stock would be expected to go to zero on any

market decline.

Most new high-tech stocks have a Beta greater than one, they offer a higherrate of return but they are also very risky. The Beta is a good indicator of

how risky a stock is.

The more risky a stock is, the more its Beta moves upward. A low-Beta stock

will protect you in a general downturn.