# Investment Case Study

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Formula Sheet for Investment Analysis

Margin Percentage = (market value of assets purchased minus amount of loan) / (market value of assets purchased)

MP = ((shares * price) – loan) / (shares * price)

2. Going Short.

Margin Percentage = ((cash from short sale + collateral) – (shares borrowed * market price)) / (shares borrowed * market price)

MP = ((shares * price) + T-Bills) – (shares * price)) / (shares borrowed * price)

3. Net Asset Value.

NAV = (market value of assets – fund liabilities) / # of shares outstanding.

4. Return on a Mutual Fund.

r = return on fund f = fees. load = front-end load for A share; otherwise load = 0.

5. One Risky Asset and One Risk-Free Asset.

E(rc) = rf + y * (E(rp) -- rf). σc = y * σp.

6. Optimal y to Maximize Utility.

y* = (E(rp) -- rf) / (A σp2)

7. Single-Factor Model statistics.

ri = E(ri) + βim + ei , and m and ei are uncorrelated.

σi2 = βi2 σm2 + σ2 (ei) .

Cov (ri , rj) = βi βj σm2 .

Corr (ri , rj) = (βi βj σm2) / (σi σi) .

8. Single-Index Model statistics.

Ri (t) = αi + βi RM (t) + ei (t), M and ei are uncorrelated.

σi2 = βi2 σM2 + σ2 (ei) .

Cov (ri , rj) = βi βj σM2 .

Corr (ri , rj) = (βi βj σM2) / (σi σj) .

9. R2 for Single-Index Model Estimated Equation.

R2 = (βi2 σM2) / (βi2 σM2 + σ2 (ei)).

or

R2 = (βi2 σM2) / σi2 .

10. CAPM Security Market Line.

E(ri) = rf + βi ( E(rM) – rf) .

11. Implied Forward Yields.

nfm = (( (1+ym+n)(m+n) / (1+ym)m ) (1/n) ) -1.

12.) Duration Pricing.

ΔP = -(D / (1+i)) * Δi * P.

13.) Equity Formulas.

Pt = Dt+1 / (k-g), where…...

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