presentation on value at risk

8/3/2019 Presentation on Value at Risk

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PRESENTATION ON VALUE

AT RISK


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MEANING OF VAR

Var is a single number, whish encapsulates wholeinformation about the risk in a portfolio.

It measures potential loss from an unlikely adverse

event in a normal market environment. It involves using historical data on market prices

and rates, the current portfolio positions, andmodels for pricing those positions.

These inputs are then combined in different ways,

depending on the method, to derive an estimate of aparticular percentile of the loss distribution.


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VAR AND DURATION

Value-at-Risk is directly linked to the concept ofduration in situations where a portfolio is exposed toone risk factor only, the interest rate. Durationmeasures the exposure to the risk factor. Value-at-Risk incorporates duration with the probability of anadverse move in the interest rate.


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EXAMPLE

The VAR of a $100 million portfolio invested in a 5-yearnote. At the 95% level over one month, the portfolio VARwas found to be $1.7 million. Can we relate this numberto the portfolio duration? The typical duration for a 5-yearnote is 4.5 years. Assume now that the current yield y is

5%. From historical data, we find that the worst increasein yields over a month at the 95% is 0.40%. The worstloss, or VAR, is then given byWorst Dollar Loss = Duration x 1/(1+y) x Portfolio Value xWorstYield IncreaseVAR = 4.5 Years x (1/1.05) x $100m x 0.4%which is also $1.7 million! Thus the value at risk is directly

related to the conceptof duration. The VAR approach,however, is more general, because it allows investors toinclude many assets such as foreign currencies,commodities and equities, which are exposed to othersources of risk than interest rate movements.


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The uses of VaR?

How much risk is a particular investment

style or asset class adding to yourportfolio?

What is the risk of both the fund's assetsand liabilities?

How and why has a portfolio's risk changedover the last measurement period?


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ADVANTAGE OF VAR

Quantifies potential losses in simpleterms (a 5% chance of a loss

exceeding $1 million) Has met with approval from various

regulatory bodies concerned withthe risks faced by financial

institutions Is versatile


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DISADVANTAGE OF VAR

Estimation difficulties, and sensitivity toestimation methods used

Potential to create a false sense of security

Tends to underestimate worst-caseoutcomes

The VaR of a specific position doesntalways translate well into the VaR of the

overall portfolio

It fails to incorporate positive outcomes,thus painting an incomplete picture


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HISTORICAL SIMULATION

Historical simulations represent thesimplest way of estimating the Value atRisk for many portfolios.

In this approach, the VaR for a portfolio isestimated by creating a hypothetical timeseries of returns on that portfolio.


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Assessment

Past is not prologue

Trends in the data

New assets or market risks


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The Model-Building Approach

The main alternative to historical simulationis to make assumptions about theprobability distributions of return on the

market variables and calculate theprobability distribution of the change in thevalue of the portfolio analytically

This is known as the model building

approach or the variance-covarianceapproach


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Position

Exposures

Volatilities

s * 2.33= 99%

Correlations VARVAR


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Daily Volatilities

252

year

day

W

!W

In option pricing we measure volatilityper year

In VaR calculations we measure volatilityper day


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Finding 1 Year VAR

1 Year VAR

= 1 Day VAR*

SQRT(250)

1 WEEK SQRT(5)

1 MONTH SQRT(21)

3 MONTH SQRT(62.5)

1 YEAR SQRT(250)

Time Adjustment


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Variance Covariance

VAR Result

Finding x%Confidence

VAR

99% VAR=VARResult

* 2.33


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Microsoft Example

We have a position worth $10million in Microsoft shares

The volatility of Microsoft is 2% perday (about 32% per year)

We use N=10 and X=99


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Microsoft Example

The standard deviation of thechange in the portfolio in 1 day is

$200,000 The standard deviation of the

change in 10 days is

200 000 10 456, $632,!


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Microsoft Example

We assume that the expected changein the value of the portfolio is zero

We assume that the change in thevalue of the portfolio is normallydistributed

Since N(2.33)=0.01, the VaR is

2 33 632 456 473 621. , $1, ,v !


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AT&T Example

Consider a position of $5 million inAT&T

The daily volatility of AT&T is 1%(approx 16% per year)

The S.D per 10 days is

The VaR is50 000 10 144, $158,!

158 114 2 33 405, . $368,v !


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Portfolio

Now consider a portfolio consistingof both Microsoft and AT&T

Suppose that the correlationbetween the returns is 0.3


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S.D. of Portfolio

A standard result in statistics statesthat

In this case WX

= 200,000 and WY=

50,000 and V = 0.3. The standard

deviation of the change in theportfolio value in one day is therefore220,227

YXYXYXWVWWW!W

222


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VaR for Portfolio

The 10-day 99% VaR for the portfoliois

The benefits of diversification are

(1,473,621+368,405)1,622,657=$219,369


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