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FNCE 443 Formula exam sheet

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Formulas Sheet
Chapter 5: Risk, Return, and the Historical Record
π‘Ÿπ‘›π‘œπ‘š = π‘π‘œπ‘šπ‘–π‘›π‘Žπ‘™ πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ π‘…π‘Žπ‘‘π‘’ π‘Ÿπ‘Ÿπ‘’π‘Žπ‘™ = π‘…π‘’π‘Žπ‘™ πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ π‘…π‘Žπ‘‘π‘’ 𝑖 = πΌπ‘›π‘“π‘™π‘Žπ‘‘π‘–π‘œπ‘› π‘…π‘Žπ‘‘π‘’ π‘Ÿπ‘Ÿπ‘’π‘Žπ‘™ =
rnom ο€½ Nominal Interest Rate
π‘Ÿπ‘›π‘œπ‘š − 𝑖
1+𝑖
π‘π‘œπ‘‘π‘’ : π‘Ÿπ‘Ÿπ‘’π‘Žπ‘™ ≈ π‘Ÿπ‘›π‘œπ‘š – 𝑖
rreal ο€½ Real Interest Rate
i ο€½ Inflation Rate
t ο€½ Tax Rate
rnom ο‚΄ 1 ο€­ t  ο€­ i ο€½ r real  i  ο‚΄ 1 ο€­ t  ο€­ i ο€½ rreal 1 ο€­ t  ο€­ i ο‚΄ t
𝜎 2 = ∑𝑠 𝑝(𝑠) × [π‘Ÿ(𝑠) − 𝐸(π‘Ÿ)]2 = Variance
E (r ) ο€½ οƒ₯ p ( s )r ( s )
s
= Expected return
Chapter 6: Capital Allocation to Risky Assets
1
π‘ˆπ‘‘π‘–π‘™π‘–π‘‘π‘¦ π‘ π‘π‘œπ‘Ÿπ‘’: π‘ˆ = 𝐸(π‘Ÿ) − 𝐴𝜎 2
π‘‚π‘π‘–π‘‘π‘šπ‘Žπ‘™ π΄π‘™π‘™π‘œπ‘π‘Žπ‘‘π‘–π‘œπ‘› π‘‘π‘œ π‘Ÿπ‘–π‘ π‘˜π‘¦ π‘π‘œπ‘Ÿπ‘‘π‘“π‘œπ‘™π‘–π‘œ: 𝑦 ∗ =
2
Chapter 7: Efficient Diversification
Expected return (proportion) E(rp) = wD E(rD) + wE E(rE)
𝐸(π‘Ÿπ‘)−π‘Ÿπ‘“
π΄πœŽπ‘2
Variance: πœŽπ‘2 = 𝑀𝐷2 𝜎𝐷2 + 𝑀𝐸2 𝜎𝐸2 + 2𝑀𝐷 𝑀𝐸 Cov(π‘Ÿπ· , π‘ŸπΈ )
wD = proportion of funds in bond fund (D)
(1 − 𝑦) × π‘Ÿπ‘“
wE = proportion of funds in stock fund (E)
E(rD) = expected return on D
Covariance: πΆπ‘œπ‘£(π‘Ÿπ·, π‘ŸπΈ) = 𝜌𝐷𝐸 𝜎𝐷 𝜎𝐸
𝑀𝐸 =
E(rE) = expected return on E
𝑆𝑝 =
y=
𝜎𝐷
Optimal portfolio
𝐸(π‘Ÿπ‘‚π‘£π‘’π‘Ÿπ‘Žπ‘™π‘™ ) = 𝑦 × πΈ(π‘Ÿπ‘ƒ ) +
πœŽπ‘ƒ = 𝑀𝐸 𝜎𝐸 + 𝑀𝐷 𝜎𝐷 when 𝜌𝐷𝐸 = 1
= 1 − 𝑀𝐷 when 𝜌𝐷𝐸 = −1
𝜎𝐷 +𝜎 𝐸
𝐸(π‘Ÿπ‘ )−π‘Ÿπ‘“
πœŽπ‘
E(rP )−rf
Aσ2P
= Sharpe ratio
= Optimal Allocation
Chapter 8: Index Models
𝑆𝑖𝑛𝑔𝑙𝑒 π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿ π‘šπ‘œπ‘‘π‘’π‘™: 𝑅𝑖 = 𝐸(π‘Ÿπ‘– ) + 𝛽𝑖 π‘š + 𝑒𝑖 𝛽𝑖 = 𝑆𝑒𝑛𝑠𝑑𝑖𝑣𝑖𝑑𝑦 π‘π‘œπ‘’π‘“π‘“π‘–π‘π‘–π‘’π‘›π‘‘ π‘“π‘œπ‘Ÿ πΉπ‘–π‘Ÿπ‘š 𝐼, π‘š = π‘šπ‘Žπ‘Ÿπ‘˜π‘’π‘‘ π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿ, 𝑒𝑖 = π‘“π‘–π‘Ÿπ‘š 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 π‘Ÿπ‘Žπ‘›π‘‘π‘œπ‘š π‘£π‘Žπ‘Ÿπ‘–π‘Žπ‘π‘™π‘’
2)
π‘†π‘’π‘π‘’π‘Ÿπ‘–π‘‘π‘¦ π‘Ÿπ‘–π‘ π‘˜ 𝑖𝑛𝑑𝑒π‘₯ π‘šπ‘œπ‘‘π‘’π‘™: π‘‡π‘œπ‘‘π‘Žπ‘™ π‘…π‘–π‘ π‘˜ (𝜎 2 ) = π‘†π‘¦π‘ π‘‘π‘’π‘šπ‘Žπ‘‘π‘–π‘ π‘Ÿπ‘–π‘ π‘˜ (𝛽2 πœŽπ‘€
+ πΉπ‘–π‘Ÿπ‘š 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 π‘Ÿπ‘–π‘ π‘˜ (𝜎 2 (𝑒)
2
πΆπ‘œπ‘£π‘Žπ‘Ÿπ‘–π‘Žπ‘›π‘π‘’ = πΆπ‘œπ‘£(π‘Ÿπ‘– π‘Ÿπ‘— ) = π‘ƒπ‘Ÿπ‘œπ‘‘π‘’π‘π‘‘ π‘œπ‘“ π‘π‘’π‘‘π‘Žπ‘  ∗ π‘€π‘Žπ‘Ÿπ‘˜π‘’π‘‘ 𝑖𝑛𝑑𝑒π‘₯ π‘Ÿπ‘–π‘ π‘˜ = 𝛽𝑖 𝛽𝑗 πœŽπ‘€
*Single index model = 𝑅 − 𝑅𝐹 = 𝐴(π‘Žπ‘™π‘β„Žπ‘Ž) + (π‘…π‘š + 𝑅𝑓 )
Chapter 9: The Capital Asset Pricing Model
2
Market risk Premium = E(π‘…π‘š ) = π΄Μ…πœŽπ‘€
π΅π‘’π‘‘π‘Ž: 𝛽𝑖 =
πΆπ‘œπ‘£(𝑅𝑖 𝑅𝑀
π‘†π‘’π‘π‘’π‘Ÿπ‘–π‘‘π‘¦π‘€π‘Žπ‘Ÿπ‘˜π‘’π‘‘πΏπ‘–π‘›π‘’: 𝐸(π‘Ÿπ‘– ) = π‘Ÿπ‘“ + 𝛽𝑖 [𝐸(π‘Ÿπ‘š ) − π‘Ÿπ‘“ ]
2
πœŽπ‘€
π‘π‘’π‘Ÿπ‘œ π΅π‘’π‘‘π‘Ž 𝑆𝑀𝐿: 𝐸(π‘Ÿπ‘– ) = 𝐸(π‘Ÿπ‘§ ) + 𝛽𝑖 [𝐸(π‘Ÿπ‘€ ) − 𝐸(π‘Ÿπ‘§ )]
Multifactor SML (in excess return): 𝐸(𝑅𝑖 ) = (𝛽𝑖 𝑀)𝐸(π‘…π‘š ) + ∑𝐾
𝐾=1 π›½π‘–π‘˜ 𝐸(π‘…π‘˜ )
Chapter 10: Arbitrage Pricing Theory and Multifactor Models of Risk and Return
𝑆𝑖𝑛𝑔𝑙𝑒 π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿ π‘šπ‘œπ‘‘π‘’π‘™: 𝑅𝑖 = 𝐸(𝑅𝑖 ) + 𝛽1 𝐹 + 𝑒𝑖
Ri = Excess return (Security), Bi = Factor sensitivity/Beta, F = Marco-factor (+ or -),
ei = Firm specific event(zero expected value)
𝛽𝑃 = ∑𝑀𝑖 𝛽𝑖 *
𝑒𝑃 = ∑𝑀𝑖 𝑒𝑖
Multifactor Model (Here,2 factors, 𝐹1 π‘Žπ‘›π‘‘ 𝐹2 ): 𝑅𝑖 = 𝐸(𝑅𝑖 ) + 𝛽1 𝐹1 + 𝛽2 𝐹2 + 𝑒𝑖
𝑆𝑖𝑛𝑔𝑙𝑒 𝐼𝑛𝑑𝑒π‘₯ π‘šπ‘œπ‘‘π‘’π‘™: 𝑅𝑖 = π‘Ž + 𝛽𝑖 𝑅𝑀 + 𝑒𝑖
Multifactor SML (here, 2 factors, 𝐹1 π‘Žπ‘›π‘‘ 𝐹2 ): 𝐸(π‘Ÿπ‘– ) = (π‘Ÿπ‘“ ) + 𝛽1 [𝐸(π‘Ÿ1 ) − π‘Ÿπ‘“ ] + 𝛽2 [𝐸(π‘Ÿ2 ) − π‘Ÿπ‘“ ]
*Two factor portfolio Risk Premium = E(R1) and E(R2)
π‘Ÿπ‘“ + 𝛽1 𝐸(𝑅1 ) + 𝛽2 𝐸(𝑅2 )
𝐹𝐹 π‘‡β„Žπ‘Ÿπ‘’π‘’ π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿ π‘šπ‘œπ‘‘π‘’π‘™: 𝑅𝑖𝑑 = π‘Žπ‘– + 𝛽𝑖𝑀 𝑅𝑀𝑑 + 𝛽𝑖𝑆𝑀𝐡 𝑆𝑀𝐡𝑑 + 𝛽𝑖𝐻𝑀𝐿 𝐻𝑀𝐿𝑑 + 𝑒𝑖𝑑
Chapter 11: The Efficient Market Hypothesis
𝐸π‘₯𝑝𝑒𝑐𝑑𝑒𝑑 π‘…π‘’π‘‘π‘’π‘Ÿπ‘›: π‘Ÿπ‘‘ = π‘Ž + π‘π‘Ÿπ‘€π‘‘ + 𝑒𝑑 π΄π‘π‘›π‘œπ‘Ÿπ‘šπ‘Žπ‘™ π‘…π‘’π‘‘π‘’π‘Ÿπ‘›: 𝑒𝑑 = π‘Ÿπ‘‘ − (π‘Ž + π‘π‘Ÿπ‘€π‘‘ )
π‘Ÿπ‘€π‘‘ = π‘€π‘Žπ‘Ÿπ‘˜π‘’π‘‘ ′ 𝑠 π‘Ÿπ‘Žπ‘‘π‘’ π‘œπ‘“ π‘Ÿπ‘’π‘‘π‘’π‘Ÿπ‘› (π‘ƒπ‘’π‘Ÿπ‘–π‘œπ‘‘), 𝑒𝑑 = π‘†π‘’π‘π‘’π‘Ÿπ‘–π‘‘π‘¦ ′ 𝑠 π‘Ÿπ‘’π‘’π‘‘π‘Ÿπ‘› (πΉπ‘–π‘Ÿπ‘š 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐), 𝑏 = 𝑆𝑒𝑛𝑠𝑑𝑖𝑣𝑖𝑑𝑦 π‘‘π‘œ π‘šπ‘Žπ‘Ÿπ‘˜π‘’π‘‘, π‘Ž = π΄π‘£π‘’π‘Ÿπ‘Žπ‘”π‘’ π‘Ÿπ‘Žπ‘‘π‘’ π‘œπ‘“ π‘Ÿπ‘’π‘‘π‘’π‘Ÿπ‘›
Chapter 14: Bond Prices and Yields
1
1
1
𝐸𝐡𝐼𝑇
π‘†π‘Žπ‘™π‘’π‘ 
πΈπ‘žπ‘’π‘–π‘‘π‘¦
π‘ƒπ‘Ÿπ‘–π‘π‘’ = πΆπ‘œπ‘’π‘π‘œπ‘› ∗ ( ) [1 − ((1+π‘Ÿ)𝑇 )] + π‘ƒπ‘Žπ‘Ÿ π‘£π‘Žπ‘™π‘’π‘’ ∗ ((1+π‘Ÿ)𝑇 )
𝑍 = 3.1 (
) + 1.0 (
) + 0.42 (
)
π‘Ÿ
𝐴𝑠𝑠𝑒𝑑𝑠
= πΆπ‘œπ‘’π‘π‘œπ‘› ∗ 𝐴𝑛𝑛𝑒𝑖𝑑𝑦 π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿ(π‘Ÿ, 𝑇) + π‘ƒπ‘Žπ‘Ÿ π‘£π‘Žπ‘™π‘’π‘’ ∗ 𝑃𝑉 π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿ (π‘Ÿ, 𝑇)
π‘π‘œπ‘šπ‘–π‘›π‘Žπ‘™ π‘Ÿπ‘’π‘‘π‘’π‘Ÿπ‘› =
πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘+π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘Žπ‘π‘π‘Ÿπ‘’π‘π‘–π‘Žπ‘‘π‘–π‘œπ‘›
πΌπ‘›π‘–π‘‘π‘–π‘Žπ‘™ π‘ƒπ‘Ÿπ‘–π‘π‘’
π΄π‘π‘π‘’π‘Ÿπ‘’π‘‘ π‘–π‘›π‘‘π‘’π‘Ÿπ‘’π‘ t
πΆπ‘œπ‘’π‘π‘œπ‘›+(𝐹𝑃−𝐼𝑃)
π»π‘œπ‘™π‘‘π‘–π‘›π‘” π‘π‘’π‘Ÿπ‘–π‘œπ‘‘ π‘Ÿπ‘’π‘‘π‘’π‘Ÿπ‘› =
𝐼𝑃
π‘…π‘’π‘Žπ‘™ π‘Ÿπ‘’π‘’π‘‘π‘Ÿπ‘› =
𝐴𝑠𝑠𝑒𝑑𝑠
πΏπ‘–π‘Žπ‘π‘–π‘™π‘–π‘‘π‘’π‘ 
Z >1.2 = vulnerability, 1.23 < Z < 2.90 = gray area , Z < 2.90 = safe
1+π‘π‘œπ‘šπ‘–π‘›π‘Žπ‘™ π‘Ÿπ‘’π‘‘π‘’π‘Ÿπ‘›
πΌπ‘›π‘£π‘œπ‘–π‘π‘’ π‘π‘Ÿπ‘–π‘π‘’ = πΉπ‘™π‘Žπ‘‘ π‘π‘Ÿπ‘–π‘π‘’ +
1+πΌπ‘›π‘“π‘™π‘Žπ‘‘π‘–π‘œπ‘›
π΄π‘π‘’π‘’π‘Ÿπ‘’π‘‘ π‘–π‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ =
π΄π‘›π‘›π‘’π‘Žπ‘™ πΆπ‘œπ‘’π‘π‘œπ‘› π‘π‘Žπ‘¦π‘šπ‘’π‘›π‘‘
2
∗
π·π‘Žπ‘¦π‘  𝑠𝑖𝑛𝑐𝑒 π‘™π‘Žπ‘ π‘‘ π‘π‘œπ‘’π‘π‘œπ‘› π‘π‘Žπ‘¦π‘šπ‘’π‘›π‘‘
π·π‘Žπ‘¦π‘  π‘ π‘’π‘π‘Žπ‘Ÿπ‘Žπ‘‘π‘–π‘›π‘” π‘π‘œπ‘’π‘π‘œπ‘› π‘π‘Žπ‘¦π‘šπ‘’π‘›π‘‘π‘ 
Chapter 15: The Term Structure of Interest Rates
(1+𝑦 )𝑛
πΉπ‘œπ‘Ÿπ‘€π‘Žπ‘Ÿπ‘‘ π‘Ÿπ‘Žπ‘‘π‘’ π‘œπ‘“ π‘–π‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘: 1 + 𝑓𝑛 = (1+𝑦 𝑛 )𝑛−1
𝑛−1
1
π‘Œπ‘–π‘’π‘™π‘‘ π‘‘π‘œ π‘šπ‘Žπ‘‘π‘’π‘Ÿπ‘–π‘‘π‘¦ 𝑔𝑖𝑣𝑒𝑛 π‘ π‘’π‘žπ‘’π‘’π‘›π‘π‘’ π‘œπ‘“ π‘“π‘œπ‘Ÿπ‘€π‘Žπ‘Ÿπ‘‘ π‘Ÿπ‘Žπ‘‘π‘’: (1 + 𝑦𝑛 ) = (1 + π‘Ÿ1 )(1 + 𝑓2 )(1 + 𝑓3 ) … (1 + 𝑓𝑛 )𝑛
Liquidity premium = Forward rate – Expected short rate
Chapter 16: Managing Bond Portfolios
π‘€π‘Žπ‘π‘’π‘™π‘Žπ‘¦ ′ π‘ π‘‘π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› 𝐷 = ∑𝑇𝑑=1 𝑑 ∗ 𝑀𝑑 𝑀𝑑 =
1+𝑦
𝑦
−
𝐷
1+𝑦
𝐢𝐹𝑑 ⁄(1+𝑦)𝑑
𝑃
′
π‘€π‘œπ‘‘π‘–π‘“π‘–π‘’π‘‘ π‘‘π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› π‘Žπ‘›π‘‘ π‘π‘œπ‘›π‘‘ π‘π‘Ÿπ‘–π‘π‘’ π‘Ÿπ‘–π‘ π‘˜:
βˆ†π‘ƒ
𝑃
βˆ†(1+𝑦)
= −𝐷 ∗ [
1+𝑦
]
π·π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› π‘œπ‘“ π‘π‘’π‘Ÿπ‘π‘’π‘‘π‘’π‘–π‘‘π‘¦ =
∗= π‘ƒπ‘’π‘Ÿπ‘π‘’π‘›π‘‘π‘Žπ‘”π‘’ π‘β„Žπ‘Žπ‘›π‘”π‘’ 𝑖𝑛 π‘π‘œπ‘›π‘‘ 𝑠 π‘π‘Ÿπ‘–π‘π‘’
π΅π‘œπ‘›π‘‘ π‘ƒπ‘Ÿπ‘–π‘π‘–π‘›π‘” π‘Ÿπ‘–π‘ π‘˜ 𝑖𝑛𝑐𝑙𝑒𝑑𝑖𝑛𝑔 π‘π‘œπ‘›π‘£π‘’π‘₯𝑖𝑑𝑦:
Chapter 18: Equity Valuation Models
𝐸(𝐷1 )+[𝐸(𝑃1 )−𝑃0 ]
𝐸π‘₯𝑝𝑒𝑐𝑑𝑒𝑑 𝐻𝑃𝑅 = 𝐸(π‘Ÿ) =
𝑃0
βˆ†π‘ƒ
𝑃
= −𝐷 ∗ βˆ†π‘¦ + 0.5 ∗ πΆπ‘œπ‘›π‘£π‘’π‘₯𝑖𝑑𝑦 ∗ (βˆ†π‘¦)2
πΌπ‘›π‘‘π‘Ÿπ‘–π‘›π‘ π‘–π‘ π‘‰π‘Žπ‘™π‘’π‘’: 𝑉0 =
𝐸
𝑃
π‘˜
𝐸
πΊπ‘Ÿπ‘œπ‘€π‘‘β„Ž π‘œπ‘π‘π‘œπ‘Ÿπ‘‘π‘’π‘›π‘–π‘‘π‘–π‘‘π‘’π‘ : π‘ƒπ‘Ÿπ‘–π‘π‘’ = ( 1) + 𝑃𝑉𝐺𝑂 π·π‘’π‘‘π‘’π‘Ÿπ‘šπ‘–π‘›π‘Žπ‘›π‘‘ π‘œπ‘“
𝐷1
1+π‘˜
π‘Ÿπ‘Žπ‘‘π‘–π‘œ:
𝐸𝑓𝑓𝑒𝑐𝑑𝑖𝑣𝑒 π‘‘π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› =
𝐷
𝐷 +𝑃
2
β„Ž
β„Ž
+ (1+π‘˜)
2 + β‹― + (1+π‘˜)β„Ž
𝑃1
𝐸1
1
𝑃𝑉𝐺𝑂
π‘˜
𝐸1
π‘˜
= (1 +
)
βˆ†π‘ƒ/𝑃
βˆ†π‘Ÿ
πΆπ‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘ πΊπ‘Ÿπ‘œπ‘€π‘‘β„Ž 𝐷𝐷𝑀: 𝑉0 =
𝑃0
𝐸1
=
1−𝑏
π‘˜−𝑅𝑂𝐸 π‘₯ 𝑏
πΉπ‘Ÿπ‘’π‘’ π‘π‘Žπ‘ β„Ž π‘“π‘™π‘œπ‘€ π‘‘π‘œ π‘“π‘–π‘Ÿπ‘š: 𝐹𝐢𝐹𝐹 = 𝐸𝐡𝐼𝑇(1 − 𝑑𝑐 ) + π·π‘’π‘π‘Ÿπ‘’π‘π‘–π‘Žπ‘‘π‘–π‘œπ‘› − πΆπ‘Žπ‘π‘–π‘‘π‘Žπ‘™ 𝑒π‘₯π‘π‘’π‘›π‘‘π‘–π‘‘π‘’π‘Ÿπ‘’π‘  − πΌπ‘›π‘π‘Ÿπ‘’π‘Žπ‘ π‘’ 𝑖𝑛 π‘π‘ŠπΆ
πΉπ‘Ÿπ‘’π‘’ π‘π‘Žπ‘ β„Ž π‘“π‘™π‘œπ‘€ π‘‘π‘œ π‘’π‘žπ‘’π‘–π‘‘π‘¦: 𝐹𝐢𝐹𝐸 = 𝐹𝐢𝐹𝐹 − πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ 𝑒π‘₯𝑝𝑒𝑛𝑠𝑒 ∗ (1 − 𝑑𝑐 ) + πΌπ‘›π‘π‘Ÿπ‘’π‘Žπ‘ π‘’ 𝑖𝑛 𝑛𝑒𝑑 𝑑𝑒𝑏𝑑
πΉπ‘–π‘Ÿπ‘š π‘‰π‘Žπ‘™π‘’π‘’ = ∑𝑇𝑑=1
where, 𝑉𝑑 =
𝐹𝐢𝐹𝐹𝑇+1
π‘Šπ΄πΆπΆ−𝑔
𝐹𝐢𝐹𝐸𝑑
𝑑
𝐸)
πΌπ‘›π‘‘π‘Ÿπ‘–π‘›π‘ π‘–π‘ π‘‰π‘Žπ‘™π‘’π‘’ π‘œπ‘“ πΈπ‘žπ‘’π‘–π‘‘π‘¦ = ∑𝑇𝑑=1 (1+π‘˜
𝐸
+ (1+π‘˜π‘‡
𝑇
𝐸)
where 𝐸𝑇 =
𝐷1
π‘˜−𝑔
𝐹𝐢𝐹𝐹𝑑
(1+π‘Šπ΄πΆπΆ)𝑑
𝑉
𝑑
+ (1+π‘Šπ΄πΆπΆ)
𝑇
𝐹𝐢𝐹𝐸𝑇+1
π‘˜πΈ −𝑔
Chapter 19: Financial Statement Analysis
𝑅𝑂𝐸 π‘Žπ‘›π‘‘ πΏπ‘’π‘£π‘’π‘Ÿπ‘Žπ‘”π‘’
𝐷𝑒𝑏𝑑
) , π‘π‘œ 𝑑𝑒𝑏𝑑(𝑅𝑂𝐴) = 𝑅 → 𝑅𝑂𝐸 = 𝑅𝑂𝐴(1 − 𝑑),
πΈπ‘žπ‘’π‘–π‘‘π‘¦
𝑅𝑂𝐴 > π‘Ÿ, πΉπ‘–π‘Ÿπ‘š π‘’π‘Žπ‘Ÿπ‘›π‘  π‘šπ‘œπ‘Ÿπ‘’ π‘Žπ‘›π‘‘ π‘‘β„Žπ‘Žπ‘› 𝑖𝑑 π‘π‘Žπ‘¦π‘  π‘œπ‘’π‘‘ π‘‘π‘œ π‘π‘Ÿπ‘’π‘‘π‘–π‘‘π‘œπ‘Ÿπ‘  π‘Žπ‘›π‘‘ 𝑅𝑂𝐸 π‘–π‘›π‘π‘Ÿπ‘’π‘Žπ‘ π‘’
𝑅𝑂𝐴 < π‘Ÿ, 𝑅𝑂𝐸 𝑀𝑖𝑙𝑙 𝐷𝑒𝑐𝑙𝑖𝑛𝑒 π‘“π‘Ÿπ‘œπ‘š 𝐷𝑒𝑏
𝑁𝑒𝑑 π‘ƒπ‘Ÿπ‘œπ‘“π‘–π‘‘
π‘ƒπ‘Ÿπ‘’π‘‘π‘Žπ‘₯ π‘ƒπ‘Ÿπ‘œπ‘“π‘–π‘‘ 𝐸𝐡𝐼𝑇
π‘†π‘Žπ‘™π‘’π‘ 
𝐴𝑠𝑠𝑒𝑑𝑠
π·π‘’π‘ƒπ‘œπ‘›π‘‘ πΉπ‘œπ‘Ÿπ‘šπ‘’π‘™π‘Ž: 𝑅𝑂𝐸 =
∗
∗
∗
∗
(𝑅𝑂𝐸) = (1 − π‘‡π‘Žπ‘₯ π‘Ÿπ‘Žπ‘‘π‘’) (𝑅𝑂𝐴 + (𝑅𝑂𝐴 − πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ π‘Ÿπ‘Žπ‘‘π‘’)
π‘ƒπ‘Ÿπ‘’π‘‘π‘Žπ‘₯ π‘ƒπ‘Ÿπ‘œπ‘“π‘–π‘‘
𝐸𝐡𝐼𝑇
π‘†π‘Žπ‘™π‘’π‘ 
𝐴𝑠𝑠𝑒𝑑𝑠
πΈπ‘žπ‘’π‘–π‘‘π‘¦
Factor 1 = Tax Burden ratio, Factor 2 = Interest-burden ratio, Factor 3 = Profit margin/ Return of sale, Factor 4 = Total Asset turnover (ATO),
Factor 5 = Leverage ratio
π΄π‘›π‘œπ‘‘β„Žπ‘’π‘Ÿ π·π‘’π‘π‘œπ‘›π‘‘ πΉπ‘œπ‘Ÿπ‘šπ‘’π‘™π‘Ž
𝑅𝑂𝐴 = π‘€π‘Žπ‘Ÿπ‘”π‘–π‘› ∗ π‘‡π‘’π‘Ÿπ‘›π‘œπ‘£π‘’π‘Ÿ
𝐸𝐡𝐼𝑇
𝐸𝐡𝐼𝑇
𝑁𝐼
π‘…π‘’π‘‘π‘’π‘Ÿπ‘› π‘œπ‘› π‘Žπ‘ π‘ π‘’π‘‘π‘  (𝑅𝑂𝐴) =
π‘…π‘’π‘‘π‘’π‘Ÿπ‘› π‘œπ‘› π‘π‘Žπ‘π‘–π‘‘π‘Žπ‘™ (𝑅𝑂𝐢) =
π‘…π‘’π‘‘π‘’π‘Ÿπ‘› π‘œπ‘“ π‘’π‘žπ‘’π‘–π‘‘π‘¦ (𝑅𝑂𝐸) =
π‘‡π‘œπ‘‘π‘Žπ‘™ 𝐴𝑠𝑠𝑒𝑑𝑠
πΏπ‘œπ‘›π‘”−π‘‘π‘’π‘Ÿπ‘š πΆπ‘Žπ‘π‘–π‘‘π‘Žπ‘™
𝑆𝐸
Chapter 20: Option Markets: Intro
Option stock = stock price – exercise price,
Profit = Final Value- Original Investment
π‘ƒπ‘Žπ‘¦π‘œπ‘“π‘“ π‘‘π‘œ πΆπ‘Žπ‘™π‘™ π‘–π‘›π‘£π‘’π‘ π‘‘π‘œπ‘Ÿ =
π‘†π‘Ÿ − 𝑋 𝐼𝑓 π‘†π‘Ÿ > 𝑋
0
𝐼𝑓 π‘†π‘Ÿ > 𝑋
{
π‘ƒπ‘Žπ‘¦π‘œπ‘“π‘“ π‘‘π‘œ 𝑝𝑒𝑑 π‘–π‘›π‘£π‘’π‘ π‘‘π‘œπ‘Ÿ = {
𝑃𝑒𝑑 − π‘π‘Žπ‘™π‘™ π‘π‘Žπ‘Ÿπ‘–π‘‘π‘¦: 𝑃 = 𝐢 − π‘†π‘Ÿ + 𝑃𝑉(𝑋) + 𝑃𝑉(𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠),
𝐢+
0
𝐼𝑓 π‘†π‘Ÿ ≤ 𝑋
𝑋 − π‘†π‘Ÿ 𝐼𝑓 π‘†π‘Ÿ ≤ 𝑋
𝑋
St = Value of stock, X = exercise price
C = Call cost, P =
2 = 𝑆0 + 𝑃
(1+π‘Ÿπ‘“ )
Put Price, 𝑆0 = π‘†π‘‘π‘œπ‘π‘˜ π‘π‘Ÿπ‘–π‘π‘’
Chapter 3: How securities are tied
Primary Market
Secondary Market
Market for newly issued securities
Investors trade previously issued securities among themselves.
Firms issue new securities through underwriter to public Issuing firm doesn’t receive proceeds and is not directly involved.
Issuer receives the proceeds from the sale.
equity crowdfunding - recent innovation for financing small start-up companies; considerably lightens the regulatory burden of firms.
Underwritten: Firm commitment of proceeds to the issuing firm (Brought deal)
Price Below Limit
Price Above Limit
Buy
Limit-Buy Order
Stop-Buy Order
Sell
Stop-Loss Order
Limit Sell Order
Types of Markets:
Direct search: Buyers and sellers seek each other
Brokered markets: Brokers search out buyers and sellers
Dealer markets: Dealers have inventories of assets from which they buy and sell
Auction markets: Traders converge at one place to trade
Chapter 5: risk, return, and the historical record data
Fundamental factors that determine the level of interest rates:
Nominal interest rate: Growth of money
-Supply of funds from savers, primarily households
Real interest rate: Growth of purchasing power
-Demand for funds from businesses to be used to finance investments in plant, equipment, and inventories
Fisher equation: Predict the nominal rate of
interest
-Government’s net demand for funds as modified by actions of the Federal Reserve Bank
Work better when inflation is more predictable
-Expected rate of inflation
Measure of downside risk:
Value at risk (VAR): Loss occurred from extreme adverse price change with some probability.
Expected shortfall (ES): Expected loss on security condition on return being on the left tail of normal distribution
Lower partial standard deviation (LPSD): SD computed using only the portion of the return distribution below a threshold
Chapter 6: Capital Allocation to risky assets
Risk-averse: Investors only consider risk-free or speculative prospects with positive risk premiums.
Portfolio is more attractive when it is expected return is higher, and its risk is lower.
Risk Averse: Rejects investment portfolios that are fair games or worse A > 0
Risk-neutral: Judges risky prospects solely by their expected returns A =0
Risk Lover: Accepts a fair game or gamble; the investor adjusts the expected return upward to take into account the “fun” of confronting the prospect’s risk
A<0
Requirements for Portfolio A to dominate Portfolio B
𝐸 (π‘Ÿ _𝐴 )≥𝐸 (π‘Ÿ _𝐡 )
𝜎 _𝐴 ≤ 𝜎 _𝐡
At least one inequality is strict (to rule out indifference between the two portfolios)
Chapter 8: Index Models
Industry version of the Index Model: Portfolio Construction and Single-Index Model
Predicting betas using these variables: Alpha and Security Analysis:
1.Variance of earnings
1.Macroeconmic estimates risk premium and market risk
2.Variance of cash flow
2.Statstical estimates beta coefficient and residual variances
3.Growth In earnings per share
3.Establish the expected return of each security absent
4. Market capitalization (Firm size)
4.Security-specific expected return forecast are derived from various security valuation model
5. Dividend yield
6. Debt-to-Asset ratio
Chapter 9:The Capital Asset Pricing Model
Extensions of the CAPM
-Identical Inputs list
-Zero Beta model -Labor Income and Other Nontraded Assets
-Multiperiod Model and Hedge portfolios
Consumption based CAPM -Liquid
Liquidity Risk: Liquidity in one stock decrease, decrease in other stock at the same time
Chapter 10: Arbitrage Pricing Theory and Multifactor Models of Risk and Return
Multifactor models: returns respond to multiple systematic risk factors and firm-specific influences (Beneficial in risk management)
Arbitrage pricing theory: Predicts SML linking expected returns to risk
APT relies on three key propositions
1.Security return can be describe by a factor model
2.Sufficient securities can diversify idiosyncratic risk
3. Well functioning security markets allow for the persistence of arbitrage opportunities
Unsystematic risk is negligible
-
Chapter 11: The Efficient Market Hypothesis
Efficient Market: Security prices reflect available information, Investor in an efficient market should expect a equilibrium Rate of return FF,CS,KS
Version of the EMH:
Weak form: Stock price already reflect all information in the history of past prices.
Test: Returns over short horizons (momentum effect) Long horizon
(reversal effect)
Semi strong-form: Stock price already reflect all publicly available information Test: P/E effect: Lower P/E ratio, higher returns. Neglected firm effect ,
abnormal return
Strong form: Stock price reflect all relevant information (Insider trading)
Test: inside info
*All versions reflect available information
Technical analysis: Research to identify mispriced securities that focus on recurrent and predictable stock price patterns and on proxies for buy or sell
pressure (EMH approved)
Fundamental analysis: Assessment of firm value that focuses on such determinants as earnings and dividends prospects, expectations for future interest rates,
and risk evaluation (EMH disapproves)
Role of portfolio management: 1. Diversification, 2. Tax considerations, 3. Risk profile of investor
Inefficient market result: systematic resource misallocation – Overvalued securities can raise cheap capital, Undervalue securities may pass up profitable
opportunities due hig cost of raising capital, Efficient market does not equal perfect foresight market
Are markets efficient:
Magnitude issue: Large portfolios can earn enough trading profits from exploitation of minor mispricing
Selection bias issue: Only unsuccessful/ successful investment are made public while good schemes are private
Lucky event issue: Ratio to big winner to big loser is really high an the loser are never heard of
Chapter 14: Bonds and prices
Callable bonds: Come with period of call protection
Convertible bonds: Exchange bonds for number of shares of the firm’s stock
Put Bonds: Holder given option to exchange for par value at some/extend for a given number of years
Floating-rate bond: bond that has interest rate that is reset periodically based to a specified market rate
Bond prices and yields: Inverse relationship between price and yield (central feature of fixed-income securities). Main source of risk is the fluctuation interest
rates. Price curve is convex and becomes flatter at higher interest rates. Longer the maturity, the more sensitive the bond’s price to change in market interest
rates.
Current yield: Bond’s annual coupon payment divided by its price.
Premium bonds: Coupon rate > Current yield > YTM
Discount bond: Coupon rate <Current Yield < YTM
Bond yield: Yield to call: Low interest rates: price of the callable is flat since the risk of repurchase is high, High interest rates: The price of the callable bond
coverage to that of a normal bonds since the risk of call is negligible
YTM:
HPR:
Determinants of bond safety
-Average return if the bond is held to maturity
ROR over a particular investment
Coverage ratio, Leverage ratios, Debt-to-equity ratio
-Depends on coupon rates, Maturity and par value
Depends on bond’s price at the end of holding period
Liquidity ratios, Profitability ratios,
Cash flow to debt to ratio
-Readily observable
Can only be forecasted
Bond Indentures:
-Sinking funds: Issuer to periodically repurchase some proportion of outstanding bonds
-Subordination clause: Restrict the amount of additional borrowing by the firm
-Collateral: Particular asset given to bondholder for a firm defaulting
Chapter 15: Term structure of interest rates
Yield curve: Relationship between yield and maturity as a function of time, key concern of fixed income investors, central to bond evaluation
Bond stripping and bond reconstitution: offer opportunities for arbitrage. Law of one price is violated
Pure Yield Curve: Uses stripped or zero-coupon treasuries and may differ significantly from the on-the-run yield curve
On-the-run Yield curve: Refers to the plot of yield as a function of maturity for recently issued coupon bonds selling at or near par value (Published by
financial press)
Spot rate: The rate that prevails today for a time period
Short rate: Applies for a given time interval (Interest rate for that interval available at
different times)
Investors require a risk premium for longer term bonds due to uncertainty about future prices (compensates short term investors)
Theories of term structure:
-The Expectations Hypothesis Theory: States forward rate equals market consensus expectation of future short interest rates. f2 = E (r2) and Liquidity
premiums are zero (Normal yield curve implies Upward sloping yield curve based on expectation that short term interest rates will increase in the long term)
-The Liquidity Preference Theory: Long term bonds are more risky (f2 > E(r2)). Predicted to be positive
Interpreting the Term Structure: Yield curve reflects expected future interest rates but forecasts are typically clouded by liquidity premiums.
An upward sloping curve could indicate rates are expected to rise and/ or Investors require large liquidity premiums to hold long term bonds
Long term rates tend to rise in anticipation of economic expansion. Inverted yield curve may indicate that interest rates are expect to fall/ signal a recession
Chapter 16: Managing bond portfolios
Interest rates sensitivity
Duration
1.Bonds prices and yield are inversely related
A measure of the average maturity of a bonds CF
2. Increase bond’s yield, smaller price change
Macualry’s duration: weighted average of the time to each coupon or principal payment
3.Long term bonds are more price sensitive that short term
Weight is applied to each payment time is proportion of the total bond value
4.As maturity increase, Pirce sensitivity increase at a decreasing rate Duration = Maturity for zero coupon bond
5.Interest rates risk is inverse to the bond’s coupon rate
Duration < Maturity for coupon bonds
6. Price sensitivity is inverse related to the YTD at which the bond is selling
Duration rules
1.Duration of zero coupon bond equals its time to maturity
4.Holding other factors constant, the duration of a coupon bond is higher when
the bond‘s Yield to maturity is lower (Selling below par < Selling at par)
2.Holding maturity constant, a bond’s duration is lower when the coupon rate is higher
3.Holding the coupon rate constant, a bond’s duration increase with its Time to maturity
Convexity: Bonds with higher convexity exhibit higher curvature in the price-yield relationship. Convexity is the rate of change of the slope of the price-yield
curve (Fraction)
Greater curvature = Gain more from price when yield falls (Vise versa). The more volatile interest rates, the more attractive this asymmetry. Investor must pay
higher price and accept lower YTM on bonds with greater convexity.
Duration and convexity MBS: Decrease in outstanding callable corporate bonds, MBS market has grown rapidly. MBS: portfolio of callable amortizing
loans.
-Homeowners may repay loans
-MBS have negative convexity Often sell for more than their principal balance -Homeowners do not
refinance as soon as rates drop.
Duration and convexity CMO: Redirects the cash flow steam of the MBS multiple classes of derivative securities call Tranches. Tranches: designed to shit
interest rate risk to investor most willing to bear the risk. -Different tranches have different coupon rates -Some may be given preferential treatment in terms
of uncertainty over mortgage prepayment speeds
Passive Management: Managers control only the risk of their fixed-income portfolio. – Two classes of passive management: Indexing strategy and
Immunization techniques (Accepted for market price but differ greatly in terms of risk exposure)
Immunization: Techniques are used to shield overall financial status from interest rate risk (Used: Pension funds, insures, banks). Duration-matched assets
and liabilities let the assets portfolio meet the firms obligations regardless of interest rate movement
Bond-Index Funds: Similar to stock market indexing but challenges in construction: difficulties purchasing each security proportion to its market value,
Many bonds are very thinly traded, rebalancing issue. Cellular approach is pursed due difficulties. Rebalancing: realign the portfolio’s duration with duration
of the obligations
Cash flow matching: Form of Immunization that requires matching cash flows of bond portfolio with obligations (Imposes many constraints on bond
selection process)
Dedication strategy: Multiperiod basis of cashflow matching: Selection of zero-coupon or coupon bonds with total cash flows in each period that match a
series of obligations. (Once and for all approach eliminates interest rate risk)
Active Bond Management: sources of potential profit:
Horizon analysis
Substitution swap: Exchange of bond for more attractive priced bond with similar characteristics
Forecasting the realized compound.
Intermarket spread swap: Switching from one segment of the bond market to another (Treasure to corporate)
yield over various holding periods.
Rate anticipation swap: Exchange between bonds of different durations in response to forecast of interest rates.
Investment horizons
Pure yield pickup swap: Moving to higher-yield, longer-term bonds to capture liquidity premium.
Analysis selects holding period and
Tax swap: Swapping two similar bond to capture tax benefits
predicts the yield curve at end of the period.
Chapter 18: Equity Valuation Model
Fundamental analysis is to identify stock that are mispriced relative to some measure of “True” value that can be derived from financial data
Limitations of book value: Shareholder are referred to as “residual claimant”, Book value are based on historical cost, while market value measure current
value (Assets and liabilities) and Market values generally will not match historical values.
Liquation value: Good representation of a “floor” for the stock’s price
Replacement cost: Cost to replace firms assets (Tobin’s q – Ratio of market
value to replacement cost [Trends towards 1])
Intrinsic values and market price: Intrinsic value it the “true value” Trading signals: IV > MV = Buy, IV< MV = Sell, IV = MV =Hold
DDM Implications: Constant-Growth rate DDM that the stock value will be greater: 1. Larger expected dividend per share 2. Lower the market cap rate, k 3.
Expect growth rate of Dividend. Stock price is expected to grow at the same rate as dividend.
Life Cycles and Multistage Growth Models: Early years – Opportunities for profitable reinvestment, Payout ratio are low, Growth is rapid. Later years –
Difficulties finding profitable reinvestment, More Competition; firms choose to higher dividend payout ratio
Present value of Growth Opportunities: Ratio of PVGO to E/k is equivalent to the component of firm value due to growth opportunities. When PVGO = 0, P 0
=E1/k. As PVGO Increasingly contributes to the price, the P/E ratio can rise dramatically. P/E ratio reflects market optimism of firms growth prospect.
P/E increase:
P/E ratio (Stock risk)
Pitfalls in P/E Analysis
As ROE increases
Holding everything else, equal risker stocks have lower P/E ratio
Denominator in the P/E ratio are
account earnings
As Plowback, b, increase, if ROE >k Risker firms have higher rate of return, that is higher k = lower P/E multiples Influenced by: Historical cost, Choices
of GAAP.
As Plowback, b, decrease, if ROE<k Not reflect economic earnings, Earnings management
As k decreases
Inflation and Fluctuate Earnings are P/E Pitfalls
Comparing the Valuation Models:
Problem with DCF
In Practice – Values from these models may differ.
Calculations are sensitive to small changes in inputs.
Analysts are always forced to make simplifying assumptions.
Growth opportunities and growth rates are hard to pin down.
Chapter 19: Financial Statement Analysis
Two broad responsibilities for Financial Manager: 1. Investment decisions (Use of capital) and 2. Financing decision
Effective use of Asset - Turnover ratio Profitability of sales - Profit margins leverage excessive - Debt ratio/Coverage ratio
Sufficient liquid- NWC/cash ratio Choosing a benchmark: 1. Compare the historic ratio 2. Compare ratios in the same industry (possibility of misleading)
Comparability problems: Accounting differences, Inflation and interest expense, Fair value accounting (Mark-to Market), Quality of earnings and accounting
practices (International)
Potential Issue (foreign firms): Reserving practices, Depreciation, Intangibles
Value Investing: The Graham Tech – Identify barging stocks: Buy common stock less than their working capital, give no weight to fixed asset, Deduct all
liabilities from Current.
Chapter 20: Options Markets Introduction
Call option: Right to buy asset for specified price, called the exercise or strike price, on or before specified expiration date. Call holder will do it if asset price
> exercise price.
Put option: Right to sell an asset for a specified exercise or strike price on or before some specified expiration date. Put will be done if the asset price <
exercise price.
In the money: Exercise produce positive cash flow, Call Option: Asset price > Exercise Price, Put Option: Asset Price < Exercise price.
Out of the money: Exercise produce negative cash flow
at the money: Exercise = Asset price
American Option: On/before expiration date
European Option: Only on expiration date
Protective put: Purchase of asset with put option on the asset. Guarantee proceeds equal/greater than put’s exercise price.
Covered call: Purchase of stock share with a sale of a call option
Straddle: buying a call and put on a stock with the same exercise price(X) and
expiration date(T)
Spread: Combination of two or more call/put option on the same stock with different prices or times to maturity. Bullish spread payoff increases, or is
unaffected by SP increase. Horizontal is different expiration date same price, Vertical Same price, different expiration date
Collar: Option strategy that brackets the value of a portfolio between two bounds
Put-call parity theorem: Proper relation between put and call prices. Violation of parity implies arbitrage.
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