FRM Exam Part II · The Investment Function in Financial Services Management

Measuring Investment Performance and Risk in a Bank Portfolio

Updated 11 October 2026 · Fact-checked

Measuring bank investment performance means comparing yield, total return and risk. Yield shows income. Total return adds price change to income. Duration and convexity estimate how value moves when rates change. Unrealized gains and losses flow to earnings or to AOCI depending on accounting classification, and AOCI can affect capital.

Understand Measuring Investment Performance and Risk

Start with income. Yield tells you the income earned on a security relative to its price. It can be a current yield (coupon ÷ price) or a yield to maturity, which includes the pull to par. Yield alone ignores price changes, so it can mislead.

Total return fixes this. It adds income and price change over the holding period, then divides by the starting value. A bond with a 4% coupon whose price falls 3% has a total return of about 1%, not 4%. Banks also look at risk-adjusted performance, such as return per unit of volatility or return relative to a benchmark, so a high return from a very risky portfolio is not mistaken for skill.

Duration measures the sensitivity of price to yield. Modified duration gives the approximate percentage price change for a 1% (100 bp) change in yield. Convexity captures the curvature that duration misses. For a plain bond, convexity is positive: price gains from falling yields exceed losses from equal rising yields. Duration alone overstates losses when yields rise and understates gains when they fall.

Unrealized gains and losses matter for earnings and capital. Under US GAAP, securities held to maturity are carried at amortized cost, so price swings do not hit equity. Available-for-sale securities are carried at fair value, with unrealized gains and losses in accumulated other comprehensive income (AOCI), part of equity but not net income. Trading securities are at fair value through earnings. Whether AOCI counts in regulatory capital depends on the bank's category. Many large banks include it in common equity Tier 1, while some smaller banks have been allowed to opt out. Rising rates therefore can cut equity without any sale.

Key formulas to remember

Current yield: Current yield = Annual coupon ÷ Current price; Ignores price change and time to maturity.
Total return: Total return = (Income + Ending price − Beginning price) ÷ Beginning price; Include reinvestment income if the question gives it.
Modified duration: Modified duration = Macaulay duration ÷ (1 + y/m); y is yield, m is compounding periods per year.
Price change with duration: ΔP/P ≈ −D_mod × Δy; First-order estimate. Works best for small yield changes.
Price change with convexity: ΔP/P ≈ −D_mod × Δy + ½ × C × (Δy)²; Use C in the same units as Δy, with Δy as a decimal.
DV01: DV01 ≈ D_mod × P × 0.0001; Value change for a 1 bp move in yield.
Sharpe ratio: Sharpe = (Rp − Rf) ÷ σp; Excess return per unit of total risk.
Portfolio duration: D_portfolio = Σ (wi × Di); Weights are market-value weights.

How to solve Measuring Investment Performance and Risk questions

Use this order for most questions on bank portfolio performance and risk.

1Identify what is asked: income, total return, rate sensitivity, or capital effect.
2List the inputs: price, coupon, yield, duration, convexity, and the size of the rate move.
3For performance, compute income plus price change, then divide by the starting value.
4For risk, convert the rate move to a decimal and apply the duration formula. Add the convexity term if convexity is given.
5Convert percentage change into a currency amount using market value, not par.
6For capital, check the accounting classification: held to maturity, available for sale, or trading.
7Decide whether the loss goes to earnings or AOCI, and whether AOCI counts in regulatory capital for that bank.
8Check the sign and the reasonableness: rates up means price down for plain bonds.

Quickest way: Duration-plus-convexity shortcut

When to use it: Use when a question gives modified duration, convexity and a yield shock and asks for the price change.

Write Δy as a decimal, for example 100 bp = 0.01.
Compute the duration term: −D × Δy.
Compute the convexity term: ½ × C × Δy².
Add them and multiply by market value.
Sanity check: the convexity term is always positive for positive convexity.

Common mistakes in Measuring Investment Performance and Risk

Treating yield as total return
Yield is quoted most often, so it feels like the answer.
Fix: Always add price change to income when the question gives ending and beginning prices.
Forgetting the sign of the price change
Students focus on magnitude.
Fix: For a plain bond, a yield rise gives a price fall. Write the minus sign in the formula.
Using 100 instead of 0.01 for a 1% move
Mixing percent and decimal.
Fix: Convert Δy to a decimal first, and keep convexity in matching units.
Dropping the convexity term or its ½ factor
Memorizing only the duration formula.
Fix: Remember the second-order term is ½ × C × (Δy)².
Assuming unrealized losses always reduce net income
Confusing fair value changes with realized losses.
Fix: Held-to-maturity securities stay at amortized cost. Available-for-sale losses go to AOCI. Only trading losses hit earnings immediately.
Assuming AOCI always counts in regulatory capital
Equity on the balance sheet is mistaken for regulatory capital.
Fix: State that it depends on the bank's category and the opt-out rules. Read the question for clues.

Worked examples

Example 1

A bank holds a bond portfolio worth $200 million with modified duration 5.0 and convexity 40. Yields rise by 100 bp. Estimate the change in portfolio value using duration and convexity.

Show the solution

Δy = 0.01.
Duration term = −5.0 × 0.01 = −0.05, or −5.00%.
Convexity term = ½ × 40 × 0.0001 = 0.002, or +0.20%.
Total percentage change = −5.00% + 0.20% = −4.80%.
Dollar change = −0.048 × $200 million = −$9.6 million.

Answer: The portfolio loses about $9.6 million. Duration alone would give −$10 million, so convexity reduces the loss by $0.4 million.

Example 2

A bank buys a bond at $98 per $100 face. It pays an annual coupon of $4. One year later the bond is priced at $97 and the coupon has been received. What is the total return, and how does it compare with the current yield at purchase?

Show the solution

Income = $4.
Price change = 97 − 98 = −$1.
Total gain = 4 − 1 = $3.
Total return = 3 ÷ 98 = 3.06%.
Current yield at purchase = 4 ÷ 98 = 4.08%.
Difference = 4.08% − 3.06% = 1.02%, caused by the $1 price fall.

Answer: Total return is about 3.06%, compared with a current yield of about 4.08%. The price decline reduced the return by roughly 1.02 percentage points.

Exam tips

Read whether the question gives duration as modified or Macaulay. Convert if needed.
When the answer options include a duration-only value and a duration-plus-convexity value, check whether convexity is given.
For accounting questions, find the classification first. It decides whether the effect is on earnings, AOCI or neither.
Use market value, not book value or par, to convert percentage moves into amounts.
Expect interpretation: say what the result means for earnings, capital or risk limits.

Practice questions from The Investment Function in Financial Services Management

Measuring Investment Performance and Risk in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Measuring Investment Performance and Risk: frequently asked questions

What is the difference between yield and total return?

Yield measures income relative to price. Total return adds the change in price over the holding period. A bond can have a high yield and a low or negative total return if prices fall.

How do unrealized losses affect bank capital?

Unrealized losses on available-for-sale securities go to AOCI, which reduces equity without touching net income. Whether this reduces regulatory capital depends on the bank's category and whether it may exclude AOCI. Held-to-maturity losses are not recognized in equity.

Why does convexity matter for a bank portfolio?

Duration is a straight-line estimate and misses curvature. Convexity corrects for this, especially for large rate moves. For a plain bond it makes gains larger and losses smaller than duration alone suggests.

Does a longer duration mean more risk?

Yes, for the same yield change a longer duration gives a larger price move. It is a measure of interest rate sensitivity, not a complete risk measure, since it assumes small parallel yield shifts.