NISM Series X-B Formula Sheet
Ten formulas, what each one is for, and a worked example.
Level 2 moves from planning to portfolios. Expect questions on combining assets, measuring risk, judging a fund manager and pricing a bond.
These ten formulas cover that ground, with a worked Sharpe ratio example.
The 10 Formulas
1
Formula
Expected return
Expression
E(R) = Σ pᵢ × Rᵢ
Use it for
Probability-weighted return across scenarios.
2
Formula
Portfolio return
Expression
R_p = Σ wᵢ × Rᵢ
Use it for
Weighted return of the assets in a portfolio.
3
Formula
Two-asset portfolio variance
Expression
σ²_p = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρσ₁σ₂
Use it for
Portfolio risk, and why diversification works.
4
Formula
Beta
Expression
β = Cov(Rᵢ, R_m) ÷ σ²_m
Use it for
Sensitivity of an asset to the market.
5
Formula
CAPM
Expression
E(R) = R_f + β × (R_m − R_f)
Use it for
Required return for an asset's market risk.
6
Formula
Sharpe ratio
Expression
(R_p − R_f) ÷ σ_p
Use it for
Excess return per unit of total risk.
7
Formula
Treynor ratio
Expression
(R_p − R_f) ÷ β_p
Use it for
Excess return per unit of market risk.
8
Formula
Jensen's alpha
Expression
α = R_p − [R_f + β_p × (R_m − R_f)]
Use it for
Return above what CAPM predicts.
9
Formula
Modified duration
Expression
MD = Macaulay duration ÷ (1 + y)
Use it for
Bond price sensitivity: ΔP% ≈ −MD × Δy.
10
Formula
Coefficient of variation
Expression
σ ÷ Mean return
Use it for
Risk per unit of return when comparing assets.
| # | Formula | Expression | Use it for |
|---|---|---|---|
| 1 | Expected return | E(R) = Σ pᵢ × Rᵢ | Probability-weighted return across scenarios. |
| 2 | Portfolio return | R_p = Σ wᵢ × Rᵢ | Weighted return of the assets in a portfolio. |
| 3 | Two-asset portfolio variance | σ²_p = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρσ₁σ₂ | Portfolio risk, and why diversification works. |
| 4 | Beta | β = Cov(Rᵢ, R_m) ÷ σ²_m | Sensitivity of an asset to the market. |
| 5 | CAPM | E(R) = R_f + β × (R_m − R_f) | Required return for an asset's market risk. |
| 6 | Sharpe ratio | (R_p − R_f) ÷ σ_p | Excess return per unit of total risk. |
| 7 | Treynor ratio | (R_p − R_f) ÷ β_p | Excess return per unit of market risk. |
| 8 | Jensen's alpha | α = R_p − [R_f + β_p × (R_m − R_f)] | Return above what CAPM predicts. |
| 9 | Modified duration | MD = Macaulay duration ÷ (1 + y) | Bond price sensitivity: ΔP% ≈ −MD × Δy. |
| 10 | Coefficient of variation | σ ÷ Mean return | Risk per unit of return when comparing assets. |
What the Symbols Mean
- w
- Weight of each asset in the portfolio; weights add to 1.
- ρ
- Correlation between the two assets' returns.
- R_f, R_m
- Risk-free return and market return.
Free account, this exam preselected.
Worked Example: Sharpe Ratio
A fund returned 14% with a standard deviation of 12%. The risk-free rate is 6.5%.
- 1
Excess return
14% − 6.5% = 7.5%.
- 2
Divide by total risk
7.5 ÷ 12 = 0.625.
- 3
Compare
A fund with a higher Sharpe ratio delivered more return for each unit of risk.
FAQs
What correlation gives the most diversification?expand_more
A correlation of −1. At +1 there's no diversification benefit at all.
Can alpha be negative?expand_more
Yes. A negative alpha means the portfolio returned less than CAPM predicts for its beta.
Is beta the same as standard deviation?expand_more
No. Beta measures market risk only. Standard deviation measures total risk.
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