CMA Final · Strategic Financial Management

Risks in Financial Market: formula sheet

Full chapter guide

Key formulas

Expected return: E(R) = Σ (pᵢ × Rᵢ); Sum of each outcome's return multiplied by its probability. Probabilities must add up to 1.
Variance: σ² = Σ pᵢ × (Rᵢ − E(R))²; Measures spread of returns around the expected return.
Standard deviation: σ = √σ²; Common total-risk measure. Same unit as returns.
Coefficient of variation: CV = σ ÷ E(R); Risk per unit of return. Use it to compare options with different expected returns. Lower is better.
Risk premium: Risk premium = Expected return on risky asset − Risk-free rate; Extra return demanded for bearing risk.
Risk management process: Identify → Measure → Respond (avoid / reduce / transfer / accept) → Implement controls → Monitor and review; Use this sequence as your answer framework for theory questions.
Total risk: Total risk = Systematic risk + Unsystematic risk; Usually measured by standard deviation of returns. In variance terms, σ² = β²σm² + unique variance under the single index model.
Expected loss from credit risk: Expected loss = Probability of default × Exposure at default × Loss given default; Loss given default = 1 − recovery rate. Use the same period for all inputs.
Current ratio (liquidity check): Current ratio = Current assets ÷ Current liabilities; A simple indicator of funding liquidity. A low value signals higher liquidity risk but is not proof by itself.
Bid-ask spread (market liquidity): Relative spread = (Ask − Bid) ÷ Mid-price; Wider spread means less liquid. Mid-price = (Ask + Bid) ÷ 2.
Forward premium or discount (annualised): (Forward − Spot) ÷ Spot × (12 ÷ months) × 100; Use direct quotes (₹ per unit of foreign currency). Positive means the foreign currency is at a premium.
Interest rate parity (approximate): Forward ÷ Spot = (1 + i home) ÷ (1 + i foreign); Use rates for the same period. Use the exact form when the question gives period rates.
Purchasing power parity (relative): Expected spot = Spot × (1 + inflation home) ÷ (1 + inflation foreign); Direct quote only. Inflation rates must be for the same period.
Money market hedge for a payable: Amount to deposit today = Foreign payable ÷ (1 + foreign deposit rate for the period); buy that at spot using rupees; Compare the rupee cost with the forward cost.
Money market hedge for a receivable: Borrow foreign amount = Receivable ÷ (1 + foreign borrowing rate for the period); convert at spot and invest in rupees; Compare the rupee value at maturity with the forward proceeds.
Approximate price change from rate change: % change in price ≈ −Modified duration × change in yield; Valid for small yield changes. Convexity corrects larger moves.
Rate gap: Gap = Rate-sensitive assets − Rate-sensitive liabilities; Change in net interest income ≈ Gap × change in rate, for a given period.
Standard deviation (probability data): σ = √[Σ p × (R − E(R))²]; E(R) = Σ p × R. Variance is σ². For past return data, divide the sum of squared deviations by (n − 1) for a sample or n for a population, as the question states.
Beta: β = Cov(i, m) ÷ σm² = ρ(i, m) × σi ÷ σm; Cov is covariance of the security with the market, σm² is market variance and ρ is the correlation coefficient.
Portfolio beta: βp = Σ wi × βi; Weights are market-value proportions and must add to 1. Beta of the risk-free asset is 0.
Macaulay duration: D = Σ [t × PV(CFt)] ÷ Σ PV(CFt) = Σ [t × PV(CFt)] ÷ Bond price; Discount each cash flow at the bond's yield to maturity. The denominator equals the bond's price. Duration of a zero-coupon bond equals its maturity.
Modified duration: MD = D ÷ (1 + y); Use y per period. For annual coupons, y is the annual yield. For semi-annual coupons, convert carefully to years.
Price change from duration: ΔP ÷ P ≈ − MD × Δy; A linear estimate that works for small yield changes. For large changes, convexity matters.
Parametric VaR: VaR = z × σ × Portfolio value × √t; σ is the return standard deviation for one period, and t is the number of periods. Common one-tailed z values: 1.645 for 95% and 2.33 for 99%. Use the z value or normal table the question gives.
Forward rate (premium or discount): Forward rate = Spot × (1 + i of quote currency × n) ÷ (1 + i of base currency × n); Interest rate parity. n is the period in years. Quote currency is the one in which the price is stated, such as ₹ in ₹/$.
Payable hedged by forward: Rupee outflow = Foreign amount × Forward rate (offer rate for buying the foreign currency); Bank sells you the foreign currency at its selling rate.
Money market hedge for a foreign payable: Deposit today = Foreign amount ÷ (1 + foreign deposit rate × n); buy it at spot using ₹; rupee cost today × (1 + ₹ borrowing rate × n) = cost at due date; Compare the due-date cost with the forward cost.
Futures hedge ratio (minimum variance): h = ρ × (σ spot ÷ σ futures); contracts = h × Exposure value ÷ Value of one futures contract; Use only when correlation and standard deviations are given.
Option hedge outcome: Effective cost = Exercise-based amount + premium (with interest, if asked); Exercise only if it is better than the spot rate on the due date.

Quick revision

Financial risk is the chance that actual financial outcomes differ from expected ones, usually to your loss.
Market risk comes from price movements in interest rates, exchange rates, equity and commodity prices.
Credit risk is the chance a counterparty fails to pay what it owes.
Liquidity risk is the difficulty of selling an asset or raising funds quickly without a large loss.
Interest rates and bond prices move in opposite directions.
A higher duration means a bond's price is more sensitive to yield changes.
Beta measures a security's sensitivity to market movements, so it captures systematic risk only.
A beta above 1 means the security moves more than the market; below 1 means less.
VaR states the maximum loss expected at a given confidence level over a given period, under normal conditions.
VaR does not tell you how large the loss can be beyond the confidence level.
A hedge reduces risk but also limits the gain if prices move in your favour, unless you use options.
Always state the recommendation after comparing hedged and unhedged outcomes.

Common mistakes

Treating risk and loss as the same thing. Fix: Define risk as uncertainty of outcomes. Loss is one possible result of that uncertainty.
Saying higher risk always gives higher return. Fix: Write that higher risk is associated with higher expected return, as compensation. Actual returns can be lower.
Calling a falling bond price due to rising interest rates a credit risk. Fix: If the issuer still pays on time and the price falls because yields rose, it is interest rate (market) risk.
Confusing liquidity risk with insolvency. Fix: Liquidity risk is a timing problem for cash or exit. A firm can have assets exceeding liabilities and still face liquidity risk.
Treating translation exposure as a cash loss. Fix: State that translation exposure is an accounting effect unless the assets are sold or cash is remitted. Transaction exposure is the cash effect.
Using the wrong side of a bid-offer quote. Fix: The importer buys foreign currency at the bank's offer rate. The exporter sells at the bank's bid rate.
Treating beta and standard deviation as the same thing. Fix: Standard deviation is total risk. Beta is only systematic risk relative to the market. A security can have a high standard deviation and a low beta.
Forgetting to divide by the bond price when computing duration. Fix: Divide the total of t × PV by the sum of PVs, which is the price at the same yield.
Treating hedging and speculation as the same thing. Fix: State that hedging reduces an existing exposure while speculation creates a new one for profit.
Using the wrong side of the bank's quote. Fix: Ask what the bank does. If you pay a foreign amount, the bank sells to you at the higher rate. If you receive, the bank buys from you at the lower rate.

Exam tips

Open theory answers with a one-line definition, then classify the risk. It earns marks quickly.
In case-based MCQs, pick the risk type from the cause in the scenario, not from words like 'risk' used loosely.
When asked to compare options, compute CV if expected returns differ. State your decision clearly in the last line.
Use the process sequence (identify, measure, respond, monitor) as headings in long answers.
Link each risk to a fitting tool: hedging for market risk, credit limits for credit risk. Examiners reward matched recommendations.
In MCQs, find the direct cause of loss first; options often include a near-miss type.
In written answers, define each risk in one line, give a rupee or company example, then add a control. This pattern earns marks.
Always say whether a risk is systematic or unsystematic when the question mentions diversification.