Integrated Business Solutions (Multidisciplinary Case Study with Strategic Management) · Advanced Financial Management

Security Valuation and Portfolio Management for CA Final

Updated 5 October 2026 · Fact-checked

Security valuation finds the fair price of a bond or share by discounting its expected cash flows at the required return. Portfolio management combines securities to get the best return for the risk taken. Solve by finding the required return with CAPM, discounting the cash flows, then judging performance with Sharpe, Treynor and Jensen measures.

Understand Security Valuation and Portfolio Management

A security is worth the present value of the cash flows you expect from it. For a bond, those are the coupons and the redemption value. For a share, they are the dividends and the eventual sale price. The discount rate is the return you demand for the risk. If market price is below your value, the security is undervalued. If it is above, it is overvalued.

Risk has two parts. Unsystematic risk is specific to a company or industry, such as a strike or a product failure. You can reduce it by diversifying. Systematic risk comes from the whole market, such as interest rates, inflation or recession. Diversification cannot remove it. Beta measures how much a security moves with the market. Beta of 1 means it moves with the market, above 1 means more, below 1 means less.

CAPM says the market pays you only for systematic risk. Required return = risk-free rate + beta × market risk premium. Plotting this against beta gives the Security Market Line. A share with an expected return above the line is underpriced. One below the line is overpriced.

Portfolio theory shows that combining securities whose returns are not perfectly correlated lowers total risk. The portfolio return is the weighted average of the returns. The portfolio risk is not the weighted average of the risks, because correlation matters.

Performance measures compare return with risk. Sharpe uses total risk (standard deviation). Treynor uses systematic risk (beta). Jensen's alpha is the excess of actual return over the CAPM return. For bonds, duration measures price sensitivity to yield changes, and convexity corrects the error in that estimate for large changes.

Key rules to remember

Bond value: V = Σ [C ÷ (1 + kd)^t] + F ÷ (1 + kd)^n; C is coupon, F is redemption value, kd is the required yield. Use the annuity factor for coupons and the single-sum factor for redemption.
Approximate YTM: YTM ≈ [C + (F − P) ÷ n] ÷ [(F + P) ÷ 2]; A shortcut estimate. Where exact YTM is asked, use trial and interpolation at two discount rates.
Constant growth (Gordon) model: P0 = D1 ÷ (ke − g); Valid only when ke > g and growth is constant forever. D1 = D0 × (1 + g).
Multi-stage dividend valuation: P0 = PV of dividends in the high-growth years + PV of [D(n+1) ÷ (ke − g)] at year n; Value the terminal price at the end of the high-growth period, then discount it back.
CAPM: ke = Rf + β × (Rm − Rf); (Rm − Rf) is the market risk premium. If only Rm is given, subtract Rf first.
Beta: β = Cov(i, m) ÷ σm² = ρim × σi ÷ σm; Portfolio beta is the weighted average of the betas of its securities.
Two-asset portfolio risk: σp² = wA²σA² + wB²σB² + 2·wA·wB·ρAB·σA·σB; Take the square root for σp. With covariance given, the last term is 2·wA·wB·Cov(A, B).
Total risk: Total risk = Systematic risk + Unsystematic risk; In variance terms, σi² = β²σm² + variance of the residual (specific) risk.
Sharpe ratio: (Rp − Rf) ÷ σp; Uses total risk. Best for comparing portfolios that are not fully diversified.
Treynor ratio: (Rp − Rf) ÷ βp; Uses systematic risk. Suited to well-diversified portfolios.
Jensen's alpha: α = Rp − [Rf + βp × (Rm − Rf)]; Positive alpha means the manager beat the CAPM return for that beta.
Macaulay duration: D = Σ [t × PV of cash flow at t] ÷ Bond price; Stated in years. Modified duration = D ÷ (1 + y), with y the periodic yield.
Price change using duration and convexity: ΔP ÷ P ≈ − Modified duration × Δy + ½ × Convexity × (Δy)²; Duration alone gives a straight-line estimate. The convexity term adds the curvature.

How to solve Security Valuation and Portfolio Management questions

Use this sequence for any valuation or portfolio question. It keeps your working in the order the examiner's marking scheme follows.

1Read the question and mark what is asked: value, required return, risk, ratio or a buy/sell decision.
2List the data and fix the units. Convert percentages, note whether Rm or the risk premium is given, and check whether dividends are D0 or D1.
3Find the required return first. Use CAPM for equity. Use the stated yield for a bond.
4Choose the model. Use the bond formula for fixed cash flows, Gordon for constant growth, and multi-stage when growth changes. For portfolios, use the weighted average for return and the variance formula for risk.
5Do the working in a clear table with year, cash flow, discount factor and present value. Show each step so partial marks are protected.
6Compare the calculated value with the market price, or the actual return with the required return, and state the conclusion in one line.
7For performance questions, compute every measure asked, then rank the portfolios on each. Say which measure uses total risk and which uses systematic risk.
8Write a closing line with the answer and the decision, such as buy, sell or hold.

Quickest way: Required return, then value, then verdict

When to use it: Use this when time is short and the question asks for a buy or sell view, or for a ranking of funds.

Compute the CAPM return in one line: Rf + β × (Rm − Rf).
For shares, apply P0 = D1 ÷ (ke − g) straight away if growth is constant. For bonds, use annuity and present value factors from the table given.
Compare value with price. Value above price means buy. Value below price means sell.
For fund ranking, compute Sharpe, Treynor and alpha in one small table. Rank on each.
If the ranks differ between Sharpe and Treynor, explain it by diversification: the fund with poor Sharpe but good Treynor carries a lot of unsystematic risk.

Common mistakes in Security Valuation and Portfolio Management

Using D0 instead of D1 in the Gordon model.
The question gives the dividend just paid, and students plug it in directly.
Fix: Check the wording. If the dividend has just been paid, compute D1 = D0 × (1 + g) before dividing by (ke − g).
Using the market return as the risk premium in CAPM.
Students forget to subtract the risk-free rate from Rm.
Fix: Always write ke = Rf + β × (Rm − Rf). Underline whether the question gives Rm or the premium.
Taking the weighted average of standard deviations as portfolio risk.
Return is a weighted average, so students assume risk is too.
Fix: Use the variance formula with correlation or covariance, then take the square root. The weighted average is correct only when correlation is +1.
Mixing up when to use Sharpe and when to use Treynor.
Both divide excess return by a risk measure, and the names look alike.
Fix: Remember S for standard deviation (total risk) and T for beta (systematic risk). Treynor assumes the portfolio is already well diversified.
Forgetting to divide Macaulay duration by (1 + y) when estimating price change.
Students use duration in years directly as the percentage sensitivity.
Fix: Use modified duration for the price change estimate. Match y to the compounding period used for the cash flows.
Applying Gordon's model when growth is higher than or equal to the required return.
The numbers are plugged in without checking the condition.
Fix: Check ke > g first. If growth is not constant, switch to the multi-stage approach.

Worked examples

Example 1

Case: A 3-year bond has a face value of ₹1,000 and pays a 10% annual coupon. Redemption is at par at the end of year 3. Investors require a yield of 12%. (a) Find the fair price. (b) Find the Macaulay and modified duration. (c) The bond trades at ₹960. Advise whether to buy.

Show the solution

Coupon = 10% × ₹1,000 = ₹100 a year. Cash flows: ₹100, ₹100, ₹1,100.
Discount factors at 12%: year 1 = 0.8929, year 2 = 0.7972, year 3 = 0.7118.
PV: year 1 = 100 ÷ 1.12 = ₹89.29. Year 2 = 100 ÷ 1.2544 = ₹79.72. Year 3 = 1,100 ÷ 1.404928 = ₹782.96.
Price = 89.29 + 79.72 + 782.96 = ₹951.96 (rounded).
Duration weights, t × PV: 1 × 89.29 = 89.29. 2 × 79.72 = 159.44. 3 × 782.96 = 2,348.87. Total = 2,597.60.
Macaulay duration = 2,597.60 ÷ 951.96 = 2.73 years (rounded).
Modified duration = 2.73 ÷ 1.12 = 2.44 (rounded).
Market price ₹960 is above the fair value of ₹951.96, so the bond is slightly overvalued at a 12% required yield.

Answer: Fair price ≈ ₹951.96. Macaulay duration ≈ 2.73 years and modified duration ≈ 2.44. At ₹960 the bond is marginally overpriced, so do not buy at this price. A 1% rise in yield lowers the price by roughly 2.44%.

Example 2

Case: The risk-free rate is 7% and the market return is 13%. The market standard deviation is 12%. Portfolio A has an average return of 15%, a beta of 1.2 and a standard deviation of 18%. Evaluate A using Jensen, Sharpe and Treynor measures, and compare with the market.

Show the solution

Market risk premium = 13% − 7% = 6%.
CAPM required return for A = 7% + 1.2 × 6% = 14.2%.
Jensen's alpha = 15% − 14.2% = +0.8%.
Sharpe ratio of A = (15 − 7) ÷ 18 = 0.444 (rounded).
Sharpe ratio of market = (13 − 7) ÷ 12 = 0.50.
Treynor ratio of A = (15 − 7) ÷ 1.2 = 6.67% (rounded).
Treynor ratio of market = (13 − 7) ÷ 1 = 6.00%.
Interpretation: A beats the market on Jensen and Treynor, which look only at systematic risk. It trails the market on Sharpe, which looks at total risk. This suggests A carries unsystematic risk that is not being rewarded.

Answer: Alpha = +0.8%, Sharpe = 0.444 against the market's 0.50, and Treynor = 6.67% against the market's 6.00%. The manager picked well relative to beta, but the portfolio is not fully diversified, so it is weaker on total-risk basis.

Exam tips

Show the required return calculation as a separate line. Examiners award marks for CAPM even if the later valuation has an error.
Always end with a decision sentence: buy, sell, hold, or which fund ranks first and why. Many students lose marks by stopping at the number.
In bond questions, use the discount factor table given in the paper and keep two decimals in the PV column so the total reconciles.
When asked to compare Sharpe and Treynor rankings, explain any difference through diversification. This is a common theory-with-numbers combination.
In case-scenario MCQs, read the conditions first: constant growth, dividend just paid, Rm versus premium. Wrong options are usually built from these traps.

Practice questions from Advanced Financial Management

Security Valuation and Portfolio Management in other exams

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

Security Valuation and Portfolio Management: frequently asked questions

What is the difference between systematic and unsystematic risk?

Systematic risk affects the whole market, such as interest rate or inflation changes, and cannot be removed by diversification. Unsystematic risk is specific to a company or industry and can be reduced by holding many securities. Beta measures systematic risk.

When should I use Sharpe instead of Treynor?

Use Sharpe when you judge the whole portfolio, because it divides excess return by total risk. Use Treynor when the portfolio is one part of a larger, well-diversified holding, because it divides by beta. If the two rankings differ, the cause is usually unsystematic risk.

What does a positive Jensen's alpha mean?

It means the portfolio earned more than CAPM predicts for its beta. It is read as the manager's skill in selection or timing. A negative alpha means the portfolio earned less than the risk justified.

Why do we need convexity if we have duration?

Duration gives a straight-line estimate of the price change, which is accurate only for small yield changes. The bond price curve is bent, so for larger changes the estimate is off. Convexity adds a correction for that curvature.

Can I use the Gordon model for any share?

No. It needs constant growth forever and a required return higher than the growth rate. If growth differs across stages, value the high-growth years separately and use Gordon only for the terminal value.