# Value at Risk (VaR)

Value at Risk (VaR) is a summary, statistical measure of total normal market risk of loss (total value that can be lost) on a certain portfolio of financial instruments at a certain confidence level. It measures how large could be potential likely losses due to “normal” movements in the market. The technique is one of the most recent techniques and was developed at JP Morgan.

Value at Risk (VaR) results is structured as follows:

“with X% certainty, company will not lose more than \$V in the next N days.”

Value at Risk (VaR) is a snapshot of a current risk level. The Value at Risk (VaR) is a floor for potential loss that can be incurred, not a ceiling. The potential loss can be VaR or higher. VaR is used to make sure that the company can handle potential losses. The potential losses cannot necessarily be prevented or, in some cases, potential losses should not necessarily be prevented due to risk/return relationship.

The results of Value at Risk (VaR) analysis are expressed as a single number \$V (VaR number) which is determined based on two parameters namely X% which refers to confidence level and N days which refers to the time horizon. \$V refers to the maximum potential loss which will occur with X% certainty over N days which is number of days in the risk period under consideration. For example, with 1% certainty over a 5 days period.

Value at risk limits can be established for specific asset categories such as foreign exchange or real estate. The limits can also be set for various levels within an enterprise such as business unit level and overall company level.

# Using CAPM (Capital Asset Pricing Model)

In addition to Gordon Model, another way to find the cost of common stock is by using Capital Asset Pricing Model (CAPM). CAPM allows us to ascertain the relationship between required return and non-diversifiable risk, which is measured by the beta coefficient (b).

Beta coefficient (b) refers to the index that measures non-diversifiable risk (risk which a company cannot eliminate through diversification). It indicates how an asset’s return will react to the changes in the market return, which in turn shows the return on a portfolio of all securities in the market.

Capital Asset Pricing Model (CAPM) is simple, as long as you know the formula and have the information necessary for the formula. The formula is as follows:

rs= Rf+(b*(rm-Rf))

Where:

rs – required return (return on a portfolio or a security)

Rf – risk free rate (e.g. rate on the U.S. Treasury bill)

b – beta coefficient

rm – market return

EXAMPLE:

If Rf (risk free rate) is 5%, beta is 2 and market return (rm) is 12%, the rs (required return or cost of common stock) can be found as follows:

Rs=5%+(2*(12%-5%)

Rs=19%

# Test yourself

Assuming we know that beta (company’s market risk coefficient) is 2, market return is 13%, risk free rate of return is 7%, current dividend is \$4 and dividend growth over the past 5 years is 5% and the same growth is expected in the future. With CAPM, find the price of the ordinary share.

SOLUTION:

First, using CAPM, we find rs:

rs= Rf+(b*(rm-Rf))

rs=7+(2*(13-7))

rs=19%

Next, we use the Gordon model (P0=D1/(rs-g)) to find the price of the ordinary share:

Po=(4*(1+.05))/(.19-.05)

Po=4.2/0.14

Po=\$30

Test yourself:

ABC’s financial manager prepared the following information. The dividend which were paid in the current year was \$5. The growth of dividends over the last 5 years were 7% and the same growth of dividends is expected to be in the future. Risk free rate is 8%, market rate is 14% and beta coefficient is 2.

Required: What is the market price of ABC’s ordinary shares?

Solution:

Firstly we need to find required return (rs) with the help of the capital asset pricing model (CAPM).

rs= Rf+(b*(rm-Rf))

rs=8+(2*(14-8))

rs=20

Next, we need to use Gordon model:

Po=D1/(rs-g)

Po=5*(1+0.07)/(0.20-0.07)

Po=5.35/0.13

Po=41.15

The price of the ABC’s ordinary share is \$41.15. Note that we determined D1 (dividend within the next period) by taking known D0 (last dividend) and multiplying it by (1+ growth rate).

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