Posts

Market Risk Problem 1 - Calculate VaR using Parametric approach

 Assume that the profit/loss distribution for XYZ is normally distributed with an annual mean of $15 million and a standard deviation of $10 million. Calculate the VaR at the 95% and 99% confidence levels using a parametric approach. Given Data Distribution : Normal. Mean ( μ \mu μ ) : $15 million (annual). Standard deviation ( σ \sigma σ ) : $10 million (annual). Confidence levels : 95% ( z = 1.645 z = 1.645 z = 1.645 ). 99% ( z = 2.33 z = 2.33 z = 2.33 ). Formula for VaR The parametric VaR formula is: VaR = ∣ z ∣ ⋅ σ − μ \text{VaR} = |z| \cdot \sigma - \mu VaR = ∣ z ∣ ⋅ σ − μ ∣ z ∣ |z| ∣ z ∣ : z-score corresponding to the confidence level. σ \sigma σ : Standard deviation (risk/volatility). μ \mu μ : Mean (expected gain/loss). Step-by-Step Calculations 1. VaR at 95% Confidence Level ( z = 1.645 z = 1.645 z = 1.645 ) VaR 95 = ∣ 1.645 ∣ ⋅ 10 − 15 \text{VaR}_{95} = |1.645| \cdot 10 - 15 VaR 95 ​ = ∣1.645∣ ⋅ 10 − 15 VaR 95 = 16.45 − 15 = 1.45  million . \text{VaR}_{95} = 16.45 -...
Post a Comment
Read more

Market Risk : Estimate VaR using a Parametric Approach

What is the Parametric Approach? The parametric approach assumes that portfolio returns follow a specific type of mathematical distribution (like a bell-shaped curve for normal distribution). Using some simple formulas, we calculate how much you could lose at a certain confidence level (like 95% or 99%). Steps to Estimate VaR 1. Get the Data You need: Portfolio value (how much your portfolio is worth today). Mean return (average return, usually based on past data). Volatility (how much the returns fluctuate, measured as a standard deviation). Confidence level (how certain you want to be about the worst-case loss, like 95% or 99%). 2. Use a Formula VaR is calculated as: VaR = z ⋅ Volatility ⋅ Portfolio Value \text{VaR} = z \cdot \text{Volatility} \cdot \text{Portfolio Value} VaR = z ⋅ Volatility ⋅ Portfolio Value Here: z z z is a number from statistics that depends on the confidence level: For 95%, z = 1.645 z = 1.645 z = 1.645 . For 99%, z = 2.33 z = 2.33 z = 2.33 . Multipl...
Post a Comment
Read more

Market Risk : Estimate VaR using a historical simulation approach

  What is VaR? Value at Risk (VaR) measures the potential loss in value of a portfolio over a defined time period for a given confidence level. It answers the question: "How much could I lose with x % x\% x % confidence over t t t days?" Historical Simulation Approach This is a non-parametric method that uses actual historical returns to estimate potential future losses. It assumes that the past distribution of returns is representative of the future. Steps to Estimate VaR using Historical Simulation Collect Historical Data Gather historical price data for the assets in the portfolio. Calculate daily returns for each asset using: r t = P t − P t − 1 P t − 1 r_t = \frac{P_t - P_{t-1}}{P_{t-1}} r t ​ = P t − 1 ​ P t ​ − P t − 1 ​ ​ where P t P_t P t ​ is the price on day t t t . Simulate Portfolio Returns Compute the daily portfolio return for each historical period. For a portfolio with n n n assets: R t = ∑ i = 1 n w i ⋅ r i , t R_t = \sum_{i=1}^n w_i \cdot r_{i,t} R ...
Post a Comment
Read more

CORPORATE GOVERNANCE AND RISK MANAGEMENT

 CORPORATE GOVERNANCE AND RISK MANAGEMENT On July 30, 2003, SOX went into full effect in the United States. This regulation had several important practical implications: (CFOs) and (CEOs) must personally verify and certify the accuracy of financial filings with the Securities and Exchange Commission (SEC).  CFOs and CEOs must attest that all disclosures provide an accurate picture of the firm.  Certain internal controls (e.g., board of director and audit committee composition) are required, and any deficiencies (including uncovered fraudulent activity) must be promptly and accurately disclosed to investors and regulators.  The firm’s reporting procedures and internal controls must be audited annually.  Audit committee member names must be publicly disclosed, and they must  be able to understand accounting principles,  be able to comprehend financial statements,  and have audit experience. key lessons learned from risk management failures during th...
Post a Comment
Read more

CREDIT RISK TRANSFER MECHANISMS

 CREDIT RISK TRANSFER MECHANISMS Credit default swaps (CDSs) are financial derivatives that pay off when the issuer of a reference instrument (e.g., a corporate bond or a securitized fixed income instrument) defaults. This is a very direct way to measure and transfer credit risk. These derivatives function like an insurance contract in which a buyer makes regular (quarterly) premium payments, and in return, they receive a payment in the event of a default. Advantages of CDSs include: Spur innovation . This enables them to fund riskier opportunities  Cash-flow potential. CDS sellers create a stream of payments that could be a significant source of cash flow. Theoretically, they can diversify the CDS contracts  across industries and geographies such that defaults in one area should be offset by fees from CDSs that have not been triggered through default. Risk price discovery. The use of a CDS enables price discovery of a specific credit risk. A CDS is a pure play on ...
Post a Comment
Read more