Posted: February 17th, 2022






Banking Risk 1


Student’s Name

Institutional Affiliation


Instructor’s Name





Value at Risk ……………………………………………………………….3

Disadvantages of Value at Risk ………………………………………………4

Historical Data……………………………………………………………….5

American Electric Power Company Inc.…………………………………….6

Baidu Inc.………………………………………………………………………7

Parametric Method……………………………………………………………8

Monte Carlo Simulation………………………………………………………9

Limitation of Value at Risk……………………………………………………11

Credit Risk…………………………………………………………………….12

Unsecured Loans ………………………………………………………………13

KVM Model……………………………………………………………………15

Interpretation of the three Models………………………………………………18









Banking Risk 1

Value at Risk

The financial element that evaluates the risk of an investment is termed as Value at Risk; this element gives the probability of losing more than a given amount in a portfolio, and it is a statistical tool aiding in the determination of the level of a possible loss that is predicted to occur in an investment portfolio over a certain time. Confidence interval, the period over which risk is assessed, and the specified amount of loss in value or percentage are the essential elements of Value at Risk (Jorion,2000)

Value at Risk (VAR) Chart


Var has its advantages, disadvantages.

Advantages of Value at Risk

Applicability- financial institutions and banks use Value at risk to gauge the risk and profitability of diverse investments and allocate risk depending on Value at Risk. These institutions use all types of assets, derivatives, shares, and bonds for their determination. (Amine & Somoue,2017).

Universal-Value at Risk is an approved mode of buying, selling, or recommending assets for it is widely used (ALBANIA,2017).

Easy to understand- the level of risk in a given portfolio is indicated by one number, and it is measured as a percentage or per unit; this makes Value at Risk to be simple


Disadvantages of Value at Risk

When diverse methods are used to calculate VaR, the difference in methods leads the same portfolio to negative values.

Assumptions– when calculating VaR, some assumptions are made; if the assumptions are incorrect, then the risk value is also incorrect.

Large portfolios– while calculating the VaR for a portfolio, the risk of return and correlations between assets must be determined; a more significant number of diversified assets in a portfolio leads to difficulty determining the Value at Risk.

I will build my portfolio using the following companies; Apple Inc. (AAPL), American Electric Power Company Inc.(AEP), Automatic Data Processing Inc.(ADP), Baidu Inc.(BAIDU), and Charter Communication Inc.(CHTR)





The historical data will be from 1st November 2016 to 30th November 2021

Apple Inc. (AAPL)













American Electric Power Company Inc. (AEP)

Automatic Data Processing Inc. (ADP)








Baidu Inc.(BIDU)


Charter Communication Inc.(CHTR)

This method is the simplest, and with the above data from my portfolio, I will calculate the Value at Risk. I will consider data for the last 3 trading years that is 750 days; with this, I will evaluate the percentage change for each risk factor on each day for this task. For the 750 scenarios, to calculate the future values, percentage change has to be calculated, and it is calculated using the current market value. In these scenarios, the portfolio will consider nonlinear pricing models.

Value at Risk = Vn(Vi/Vi-1)

Therefore, Vi represents a variable number in(i) days when the historical data was taken. The historical data presented above, including the histogram, will be used to calculate the Value at Risk; for this case I picked, American Electric Power company Inc., we calculate as follows

750(3/3-1), with this the VaR is 95%, this indicates that when we make losses, we will not exceed 5%, this shows that if we invest, for example, $400, then our surety is 95% confidence and if we make losses it will not be more than $20

Parametric method

It is a method that partakes a normal distribution; in return, it is also termed the variance-covariance method. Estimation in this method is used to determine standard deviation and the expected return. When measuring risk problems in distributions, it is a suitable method; however, it is unreliable for a minimum sample size.

With this, we are going to use sales to determine the Value at Risk of our portfolio

company First-year Second-year Calculation
Apple Inc. 24533 20289 -0.17299
American electric company Inc. -114.3 -98.6 -1,.8626
Automatic Data processing Inc. 1695 0 -1
Baidu Inc. 9147 28831 2.1
Charter -Communication Inc. 407 699 0.717

To calculate, we get the sum of the weights multiplied by the initial growth rate of each company. The VaR values in these methods are not specific this is because the parametric method has the following limitations, it assumes that the distribution returns are expected, this is not correct for in some cases, the assets looked into have skewed return distributions, another limitation is that it cannot work appropriately for nonlinear assets for example options which have stable volatilities hence leading to a misleading VaR.

Monte Carlo simulation

VaR of a portfolio can be calculated using this method. This method solves random variables by giving the probability of the different results, which are hard to is simple to understand the uncertainty and the level of risk in predicting and forecasting models

Steps of Finding Value at Risk using Monte Carlo simulation

The first step getting (t) is the time horizon, and with this, it is divided into small periods, discretization a process of pricing continuous financial markets is applied once the time horizon has been divided into small periods

The next  move is to get a random number, generated from random number engine, and after the end of the first price increment, the portfolio is updated


Having written the formula, therefore Ri is the return on the prefix day, the stock price, on the other hand, is denoted by (Si) on an ith day, when the stock price is added to one, it represents the stock price on a day added to one, time is represented by delta, volatility which is the standard deviation is denoted by stigma, while (mu) is the sample mean of the stock price, epsilon is a random number generated from a normal distribution.

Step three to four is a repetition of step two. Ranking from the smallest to most considerable stock prices occurs on the fifth step.

Conditional Value at Risk (CVaR)

Conditional Value at Risk can be termed as the average value at risk or the mean shortfall. It is an extension of Value at Risk. Conditional Value at Risk helps calculate the average losses incurred beyond the Value at Risk point of distribution. When CVaR is small, then it is a better value.


Having calculated the Value at Risk using the above methods, it is clear that the methods have different limitations. The first value from the first method gave a VaR of 95%, while the second method gave a VaR ranging from 95-99%; with this, it is evident that computation of Value at Risk using this method has some limitations. We now look into the strengths of VaR.

The strengths of VaR

VaR is a measure that is crucial in estimating market risk in a forward-looking scenario; VaR changes instantly with the changes in market volatilities and market risk; it does not assume that the manager style stays the same over aims at gaining a single figure to the potential loss across different classes of the security market


Limitations of VaR

Value at risk can be misappropriated- VaR a time gives a false sense of security, that is, by looking at the risk exposure. In the real business world, a difference of 1% is significant, and even if one gets a 99% parameter, it is not as effective as it seems.

Value at risk does not measure worst-case loss in the outside world; a difference of 1% means that it is about two to three full trading years that the company incur a loss, thus the loss gets higher than the VaR amount Another major setback is that VaR does not mention the of losses within the 1% trading days and does not give a platform for maximizing possible losses. The loss incurred during the 2-3 days in a year can liquidate the company.

It is hard to calculate with considerable computing the Value at Risk of a portfolio, estimates of return and volatilities of each set of assets and correlations of the portfolio is taken into consideration. With the large number and diversified assets dealt with by a company, it is tedious to find the accurate VaR.

It does not add up– The VaR portfolio of apple and Bindu companies does not equal the VaR of a portfolio containing Apple and American electric companies.

Different value at risk methods leads to different results– to calculate VaR, different methods are used which each formula gives a different value.

VaR is based on assumptions– the values obtained while computing the Value at Risk of a portfolio are based on assumptions; therefore, the values of VaR cannot be something to go by






Credit Risk

Credit risk is when a loss is incurred when a borrower borrows a loan and fails to repay the loan or meet the contractual obligations. Previously, it was known as a risk a lender may not receive the owed principal and interest, which comes up while interpreting the credit default risk, concentration risk, and country risk are the three types of credit risk (Crouhy& Mark,2000).

Loan Company name Maturity Repayment value at maturity $m Interest
1 Wallmart Inc. 5 12 6%
2 Vallero energy 4 10 7%
3 Nike Inc. 3 8 5%


Unsecured loan

In unsecured loans the borrower does not place a security; it is also known as good faith loans or signature loans. Personal loans, unsecured credit cards and student loans are some of the types of unsecured loan. This type of loan can readily accede through online and government-backed lenders, and it is easy to apply for the loan than the secured loans (Chen & Ho,1998).

Unsecured loans range from as low as $1,000-$100,000, which can be used for various purposes, after approval the disbursement of funds starts immediately and some are given fully, the interest therefore starts accruing within the entire period of the loan. Payments are made per month and are deposited to three major credit bureaus.


Assumptions made in coming up with the estimations

The information available– with the comprehensive information from the internet and the companies’ website, it is easy to get the financial position of the above companies, and the data are accurate

Time of calculation– The calculation made on the above information and figures follows the date given (Gorton & Pennacchi,1995).

Income-on this case, the monthly income amount is used for the calculation; the amounts that do not fall under the period of calculation are converted into a monthly amount by having the equivalents of months and for this case an assumption is made that a year has twelve months, fifty-two weeks and haves twenty-six fortnights

Expenses –the calculation considers the number of repayments on any existing loan(s); this impacts the interest rate. when the repayments are more minor, for example, Wallmart Inc., the loan given is higher than the other companies

Interest rates– with the above data and figures, interest rates per company differ because the interest rate is subject to the verified information given during the application.

Interest and repayment cycles –the assumption made here is that all the repayments are payable and the monthly interest rate is charged on the same day.

Fees –on this, I have not included any charges or fees that are applicable sometimes.

Rounding –the amounts have been rounded off to the nearest dollar.

When calculating the credit rating of a firm for the first time, (t) will represent time and when there is multiple of years the time (t) will be denoted by figure for example one year will be (t1), year two will be (t2). and the sequence takes that order. On the formula, S will denote the rating space with state1 and N will represent the best and worst credit quality in their respective orders; when the assets of a company are lesser than the liabilities then in the equation (0) will be used to denote this case. Frey is the rating process that counts on several credit factors. (Magzanov, 2019).

St j d t Xt dt j N,

Once this equation has been formulated we move to; (MDF) of X by 1 () () F x PX x i = £.  Which shows the marginal distribution of functions

An assumption is made that X has a multirative distribution and the values of Xi are observed as a shift in the value of assets for obligor (i), which is spread over the horizon interest. 1 i d is picked so that PDi is the same as the classical trends observed by the default rate of companies falling under the same credit quality base

With the calculation and substitutions of the matrixes, we get the expected shortfall to be 89,728


The matrices tend to be diagonally dominant, meaning there is no migration most of the time. The matrix can be generated in line with the systematic component or aggregation scheme of the credit quality in a year. Once this is done, a specification of the risk horizon is made, and it is usually one year. Still, modification is extended to 10 years, preferably when concerned about the risk profile, which occurred over a long period and needs to be long-dated (Walter & Jones, 2018). Once this is done, the forward pricing model is specified, and it includes a set of percentages which in essence is the value of the instrument, forward discount curve at the risk horizon(s), and the case default. The final stage is the rating of the forward distribution in portfolio changes.

Credit metrics estimate the interrelationship between the equity returns of obligors. The credit horizon of a year is generated entirely through the distribution of the portfolio through credit metrics formula. The thresholds of asset return are derived for each rating and estimation between each pair of the order to get the assets correlation, equity correlations are used in order to stand in for assets which are not observable

Forward value is calculated as follows, the portfolio value is multiplied by the sum of the promised return, whereby the promised return is the same as the expected value and expected loss is calculated by subtracting the expected value from the forward value

The spreads in investment bonds, increases with maturity, while the low grade tends to get wide at the short end of the curve than at the long end (Zokirjonov,2018).


KVM model


Computation of both complicated and straightforward company’s default risk can be calculated using KVM, having specified time horizon, the units that are needed in the standard deviation are used to bring up the beginning point of the company. Value and the volatility of a company’s equity are the major inputs in estimation of credit quality. KVM model takes the company’s equity as the standard option based on the value of its assets; liabilities are used as the price of a call option. An assumption is that default will happen when a company’s capital assets are less than its liabilities.

Newton iteration method is used, and once it is simplified, we get;

DD= (V-D/Vδ),

Shortfall =89,070

The standard deviation –to- default is reflected by DD, and in this the value of assets of a company are distributed


COMPANY return Mean return weight Weighted return
Wallmart 0.06 1.2 0.03 0.012
Vallero energy 0.07 1.4 0.03 0.014
Nike 0.05 0.10 0.03 0.010


Given confidence of 99%, 1% of the losses will exceed VaR.

We find the expected shortfall’s expected value (average) of the bottom 5% of portfolio gains. the expected shortfall = 89,090

In this case, we are using VaR, with a sign convention that losses are stated as a positive number.


Our VaR of 36,890 has been exceeded by the expected shortfall of 89.090. we are dealing with a (1%) loss; therefore, we run enough iterations to a sample of sufficient extreme data points for a better result. at this point, it is essential to take into consideration the selection of return probability distribution; there might be an over or underestimate of the loss magnitude that is possible

Expected shortfalls expand on VaR to bring out the idea of adverse losses that VaR fails to show; however, it is imperfect while showing the absolute risk. It is just an average of the extreme losses. That said and done, it can be a helpful step beyond VaR.


With the above computation, we find that all the methods are an estimate and the difference is minimal, there; my expectations were met, the difference gets in due to;

The credit risk estimation method is different across each type of model used for data management. Credit metrics data are based on historical transition matrices. On the other hand, the primary data for KVM are assets which include stock prices, risk-free rate liabilities, and risk liabilities (Tian & Novotný,2017). The correlation of assets is also another factor that have an impact on the models. When mortalities are tabulated, they form a source of estimating credit risk model in line with the distribution in the default rate. when a bond creditworthiness changes, it is possible to explain the credit event and the models describe it individually.

. KVM method evaluates the change as a move in the position to default, of which rapidly turns into the value of EDF

On the other hand, the credit metrics model places credit events at a state with rating migration. The frequency of an event happening in KVM is greater than the events in credit metric (Frey & McNeil,2002). The volatility of credit events in the credit metrics model is started by default probability based on historical data, when there is change in the market value and volatility, then the expected frequency of failure in KVM changes accordingly. KVM structure considers return rates as constant parameters.

In contrast, in an extended KVM, the rates are beta distribution. At the same time, on credit metrics, a diverse rate of recovery estimations, the beta distribution on this model contains a beta variable that is random. Credit metrics hand in hand takes into consideration the stimulation obtained through Monte Carlo functions. KVM admits analytical solutions like the credit risk model, but only a few in credit metrics.



ALBANIA, K. (2017). ANALYSIS OF INTERNATIONAL RISK MANAGEMENT STANDARDS (ADVANTAGES AND DISADVANTAGES). European Journal of Research and Reflection in Management Sciences Vol5(3).

Amine, N. B., Rouggani, K., & Somoue, N (2017). Understand current methods of credit risk assessment to understand their advantages and disadvantages.

Chen, S. S., Yeo, G. H., & Ho, K. W. (1998). Further evidence on the determinants of secured versus unsecured loans. Journal of Business Finance & Accounting25(3‐4), 371-385.

Crouhy, M., Galai, D., & Mark, R. (2000). A comparative analysis of current credit risk models. Journal of Banking & Finance24(1-2), 59-117.

Frey, R., & McNeil, A. J. (2002). VaR and expected shortfall in portfolios of dependent credit risks: conceptual and practical insights. Journal of banking & finance26(7), 1317-1334.

Gorton, G. B., & Pennacchi, G. G. (1995). Banks and loan sales marketing nonmarketable assets. Journal of Monetary Economics35(3), 389-411.

Jorion, P. (2000). Value at Risk.

Magzanov, S. (2019). Copula functions in Credit Metrics’ VaR estimation.





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