Portfolio Management - CA Final SFM

Portfolio Management is concerned with effective management of Investment in securities selection & reshuffling of securities to optimize returns to suite the objectives of an investor.

Objectives of Portfolio Management

Security/Safety of Principal amount

Stability of Income

Capital Growth

Marketability

Liquidity

Diversification

Favorable Tax Status

Basic Formulas in Standard Deviation

S. No.	Name of Formula	Formula		Remarks
1.	Standard Deviation (Based on Historical Data)	σx =	√ (∑d2x)/n	Where d2x = (X – Average Return) Average Return = (∑x1 + x2 + ……….xn)/n
2.	Standard Deviation (Based on Probable Data)	σx =	√ (∑Pd2x)	Where, P is probability
3.	Variance	=	σ2
4.	Coefficient of Variation	=	σ E(R) Or          σ          .    Average Return	In words, Standard Deviation Expected Return Or Standard Deviation Average return
5.	Range	=	Highest Return – Lowest Expected Return
Selection of Best Portfolio Lower Standard Deviation, Variation, Coefficient of Variance and Range will have lower Risk. Security with Higher Return at same level of Risk (Standard Deviation). Security with lower Risk (Standard Deviation) with same level of Return. Security with different risk (Standard Deviation and Return then security with lower coefficient of Variation will be preferred.

Return of Portfolio

E(R_P) = E(R_A) x W_A + E(R_B) x W_B + ………

Where,

E(R_P) = Expected Return From Portfolio

E(R_A) = Expected Return from Security A

W_A = Weight of Security of A

When 2 Securities in Portfolio

σ_P = √(σ_A² w_A² + σ_B² w_B² + 2 σ_Aσ_Bw_Aw_B x r)                     

or

σ_P = √(σ_A² w_A² + σ_B² w_B² + 2 w_Aw_B x COV_(A,B))

When 3 Securities in Portfolio

σ_P = √(σ_A² w_A² + σ_B² w_B² + σ_C² w_C² + 2 σ_Aσ_Bw_Aw_B x r + + 2 σ_Aσ_Cw_Aw_C x r + + 2 σ_Cσ_Bw_Cw_B x r)                      

or

σ_P = √(σ² w_A² + σ² w_B² + 2 w_Aw_B x COV_(A,B) + 2 w_Bw_C x COV_(B,C) + 2 w_Aw_c x COV_(A,c) )

r_(A,B) = COV_(A,B)/ σ_Aσ_B

COV_(A,B) = (∑d_A x d_B)/n      or   ∑d_A x d_B x P

If r = 1, then

σ_P = σ_Aw_A + σ_Bw_B  

If r = -1, then

σ_P = σ_Aw_A - σ_Bw_B

Beta of Security (Sensitivity of Portfolio Means Beta of Portfolio)

β = (Change in security Return)/(Change in Market Return)

or

β = (COV_(S,M))/ σ_M² 

or

β = r_(S,M) x (σ_S/ σ_M)

Beta of Portfolio

β_P = β_AW_A + β_BW_­B + ………………..

Overall Beta/Beta of Firm/Assets

If No Tax

β_o = β_E x [E/(E + D)] + β_D x [D/(E + D)]

If nothing is mentioned about β_D then β_D = 0

If Tax

β_o = β_E x [E/{E + D(1- tax rate)}] + β _D[{D(1 – tax rate)}/{E + D(1 – tax rate)}]

β_o = β_E x [E/{E + D(1- tax rate)}] + 0

β_E = β_o x [E + D(1-tax rate)/E

Where,

β_o = Overall Beta   = β_U (Beta Unlevered)

β_E = Beta of Equity = β_L (Beta Levered)

β_D = Beta of Debt

E = Equity

D = Debt

 

SML (Security Market Line) Equation

R_e = R_f + β(R_m – R_f)

Sharp Ratio (Market Risk Premium)

Sharp Ratio = (R_P – R_f)/σ_P

Alpha

Alpha = E(R) – CAPM

If Alpha is positive then stock is undervalued and if alpha is negative then stock is overvalued and if Alpha = 0 then fairly valued.

Characteristic Line (CL)

Y = a + bx

Y= Return from Stock

A = Intersect

B = Beta

X = return from stock if return from market is zero

Capital Market Line (CML)

σ_P = σ_Mw_m + σ_Rfw_Rf

E(R_P) = R_f + σ_P[(R_m – R_F)/ σ_m)

W_m = σ_P/ σ_m

Arbitrage Pricing Theory (APT)

E(R_P) = R_f + β₁(R_m – R_f) + β₂(R_m – R_f) + β₃(R_m – R_f) + …………………

Where,

β₁ = Beta of factor 1

β₂ = Beta of Factor 2

β₃ = Beta of factor 3

If Factor Risk Premium or (R_m – R_f) is not defined then ,

FRP = (Actual Value – Expected Value)

R_M or R_S = [(Dividend + Capital Gain)*100]/Initial Investment

Weight of Security when r is other than 1 & -1

W_A = (σ_B² – COV_(A,B))/ σ_A²  + σ_B² – 2 COV_(A,B)

W_B = 1 - W_A

If Investment amount is specified then weighted average should be taken.

Total Risk (σ_S²) = Systematic Risk (β_S² x σ_m²) + Unsystematic Risk (Random Error)

r² = (Systematic Risk)/(Total Risk)

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