IndividualReportVeronika Prokhorenko

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Feb 20, 2024

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Veronika Prokhorenko Individual Report Case 1- CALA INVESTMENT FUND What is the Problem? CALA INVESTMENT FUND is a private equity firm that specializes on infrastructure investments.They have a choice between 3 independants projects and we want the lowest risk possible for our investment in order to make the most informed decision: the company decided to calculate the value at risk (VaR) and their expected shortfall (ES) at 95% using historical simulation. They will use for that the daily return of each project during one year The budget is $100,000,000 to invest in the projects Identify Strategies ●Accept risks (No diversification) ●Use diversification ○Balanced ■⅓ allocations to each ○Quasi ■Finding the allocations that provide the best balance of ER and ES So, if the managers accept the risk, there will be no use diversification. We can choose the biggest expected returns, or the lowest value at risk and Expected Shortfall. Since we accepts the Risk, we will choose the biggest expected returns. A plus is that due to the CoronaVirus financial losses are expected. Accepting the risk is cost effective. However, risk management is futile during this period due to the coronavirus. It is extremely unpredictable during this time. Accepting risk could also mean financial loss . Using group’s Excel: they will Choose Project B, which has the biggest VAR and Expected shortfall, but also the biggest Expected return. The other option is diversification If we want to diversify, we need to find what weight we have to invest in each projects to have the lowest possible Expected Shortfall for the highest expected return. Using Excel, at Equal Weight, we have the following results:

Now Using Excel Solver for the minimum Expected Shortfall, we have: (from the group’s presentation) Portfolio Var CALA Hedge Fund Manager’s need to decide what the optimal portfolio is vis-a-vis expected risk and return. The optimal portfolio selected will need the highest Sharpe Ratio. The managers will need to maximize position while minimizing the risk. This could also be done by hedging; and implemented by utilizing 10 Year Bonds. This will allow for a risk free rate. Implement Solution Diversify (quasi) -Invest in all three projects, allocating the weights to properly balance ER and ES -Using excel solver, this is 99% in Project A and limited weights to Projects B and C Evaluate Outcomes -Diversification (quasi) helps us to reduce a lot of our Expected Shortfall. -It helps us to reach the best balance between expected returns/Expected Shortfall. -ER about $2 million with ES at $7.7 million -Compared to heavily focusing on Project A: ER about $1.4 million with ES at $4.9 million -For this we have to invest mostly on Project A (99%)

-This solution avoids accepting the risk because ES and VaR are just too big -We use money of our investors to invests in this projects. Therefore efficient portfolio balancing (using Expected Shortfall) is the best approach for us Second Case Slavic Investment Co. Slavic Investment Co. is a wealth Management Firm who is responsible for TAX HARVESTING IRA, ESTATE PLANNING, 401K, COLLEGE SAVING PLAN, TRUST and MORE. Among their staff are Actuaries, economists, financial advisors, forecasters, traders and portfolio managers. In the event of a crash, the company promises safety! Risk Management Value At Risk is a commonplace on Wall Street . Its simple to apply and easy to calculate using historical data . Also, its easy to match risk preference to the clients’ VAR is all about 95% Confidence, monthly returns, and its also at most lose of 5% Now, lets recollect the recent events which can affect the success and financial well-being of the company: So, that’s what happened February 24-28 th : -Covid-19 Crisis intensifies -Oil prices shot down -Gold and U.S. Treasuries (Safe Havens) increase in value -S&P 500 dropped 11.49% -Dow Jones dropped 12.36% -3 Trillion Wipeout in one week Problem The company clearly has a dilemma: is the Value at Risk model inaccurate? It projected at most 5% lost in 1 month! Yet we saw a 10% lose in one week…Which strategy gonna help them? Solutions We can either proceed with no change and Accept the risk or rebalance to less risky portfolio, or use expected shortfall system. In a no change situation…We just keep VaR. If anything, investors will come back, and the market will be back up! In case of rebalance …We can reconstruct portfolios and include less risky assets such as fixed income. However…This will lower our expected loss in the VaR system and we lose out on bigger returns. Another case would be expected shortfall: •Conditional Var •Calculates expected loss given that the loss is greater than the VaR level •Harder to back test compared to VaR •More Complex •Provides a more extreme loss figure Implementing •Shorter horizon •1 month -> 1 week

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•More emphasis on the tails •5% of the extremes •Provides a better lose estimate •Weekly Expected Loss Evaluation: No change is the best solution. Case 3. Value at Risk Application Market risk is the risk of loss of value on financial instruments arising from changes in market parameters, the volatility of these parameters, and the correlations between them. These parameters include, but are not limited to: exchange rates interest rates the price of securities (equities or bonds) commodities derivatives and other assets. Define the problem The Market Risk Department of Societe Generale is independent from the business and is in charge of assessing the limit requests submitted by the different businesses. These requests are within the framework of the overall limits authorized by the Board of Directors and General Management.

One team from Market strategy department is requesting access to a portfolio containing the purchase of 1000 IGSB and FLTR and sale of 300 JNK and 200 HYG. All of these assets are bond ETFs and are correlated with the Market Index. Should we access it or not? Indentifying & Evaluating Strategies Expected Shortfall is a measure that produces a better incentive to the trader in comparison to the Value at Risk. It is also referred to as a conditional VaR or Tail loss. VaR asks the question ‘how bad can things get?’, expected shortfall asks ‘if things do get bad, what is our expected loss?’. Value at Risk: • • Monotonicity : if a portfolio has lower returns than another portfolio for every state of the world, its risk measure should be greater. • • Translation invariance : if we add an amount of cash K to a portfolio, its risk measure should go down by K. • • Homogeneity : changing the size of a portfolio by a factor λλ while keeping the relative amounts of different items in the portfolio the same should result in the risk measure being multiplied by λλ. • • Sub-additivity : the risk measure for two portfolios after they have been merged should be no greater than the sum of their risk measures before they were merged. The first three conditions are straightforward given that the risk measure is the amount of cash needed to be added to the portfolio to make its risk acceptable. The fourth condition states that diversification helps reduce risks. When we aggregate two risks, the total of the risk measures corresponding to the risks should either decrease or stay the same. VAR satisfies the first three conditions, but it does not always satisfy the fourth • Regulators make extensive use of VAR and its importance as a risk measure is therefore unlikely to diminish. However, expected shortfall has a number of advantages over VAR. This has led many financial institutions to use it as a risk measure internally Solution 95% Var For investors, the risk is about the odds of losing money, and VAR is based on that common- sense fact. By assuming investors care about the odds of a really big loss, VAR answers the question, "What is my worst-case scenario?" or "How much could I lose in a really bad month?"

Now let's get specific. A VAR statistic has three components: a time period, a confidence level and a loss amount (or loss percentage). Keep these three parts in mind as we give some examples of variations of the question that VAR answers: •What is the most I can - with a 95% or 99% level of confidence expect to lose in dollars over the next month? • What is the maximum percentage I can - with 95% or 99% confidence - expect to lose over the next year? Historical Price of Each Assets 2/4/19 3/26/19 5/15/19 7/4/19 8/23/19 10/12/19 12/1/19 1/20/20 3/10/20 4/29/20 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 Historical P/L Source: Nasdaq.com IGSB FLTR JNK HYG Portfolio VaR: Age-weighted Historical Simulation

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Portfolio Var IGSB FLTR JNK Values $54,185 $25,420 $-31,481 Weights 166.32% 78.03% -96.63%

Implement •Market Risk Department negotiate with the manager from Front Office, the manager ask for the loss limit within 2%. Thereby, this portfolio cannot be granted. •There are several options left for the Market Strategy Department • Rebalance • Cover New Assets with Lower Loss Portfolio VAR – implement The role of a portfolio manager is to choose a portfolio that represents the best combination of expected risk and return The optimal portfolio has the highest Sharpe Ratio : Rebalance

Evaluate solution Historical Price Simulation Second, the use of a 99% confidence interval does not take into account losses arising beyond this point; VaR is therefore an indicator of the risk of loss under normal market conditions and does not take into account exceptionally significant fluctuations. In other words, Value at Risk is not an effective tool to detect potential financial Crisis. Using the Historical Price Method is not viable as it doesn’t take into account the uncertainty of future returns due to an external factor. According to Nicklas Norling and Daniel Selling’s research article, An empirical evaluation of Value-at-Risk during the financial crisis, they applied our models on S&P 500 with 786 observations between 2005-12-28 and 2008-12- 31, divided into an equally sized tranquil and crisis period. We evaluated the models by using the backtesting framework set up by Kupiec’s test. Based on our chosen methods we conclude that VaR have not worked during the financial crisis due to the high LR statistic for each approach along with insignificancy stated by the Kupiec’s test for both confidence levels. This means that VaR is proven to be serious destabilizing during times of crisis.

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Evaluate Outcome Rebalance - Using Sharpe/MVaR Ratio Thus, Market Strategy Department can rebalance this portfolio by slash the weight of IGSB and increasing the weights of JNK and HYG to make ratio of these assets equally. Thus portfolio will exhibit the lowest portfolio VaR.If not, this team needs to cover new assets to lower down its VaR.