# Key formulas ```Key Formulas
Present value of a cash flow stream
-
𝑃𝑉# = %
'./
𝐶'
(1 + 𝑟 )'
Future value of a cash flow P0 at date t
𝐹𝑉 = 𝑃𝑉# &times; (1 + 𝑟)'
Present value of a perpetuity starting in date 1
𝑃𝑉# =
𝐶/
𝑟
Present value of an annuity starting in date 1
𝑃𝑉# =
𝐶/
1
&times; 21 −
4
(1 + 𝑟 )𝑟
Present value of a constantly growing perpetuity starting in date 1
𝑃𝑉# =
𝐶/
𝑟−𝑔
Present value of a growing annuity starting in date 1
𝑃𝑉# =
𝐶/
1+𝑔 &times; 61 − 7
8 9
𝑟−𝑔
1+𝑟
9
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Measures of risk for individual assets
Variance:
C
𝑉𝑎𝑟 (𝑅&lt; ) = 𝜎&lt;? = 𝐸 (𝑅&lt; − 𝑅A)? = % 𝑝&lt; &times; (𝑅&lt; − 𝑅A )?
&lt;./
Standard deviation (volatility):
𝑆𝐷 (𝑅&lt; ) = 𝜎&lt; = F𝜎&lt;?
Covariance:
𝐶𝑜𝑣I𝑅&lt; , 𝑅K L = 𝜎&lt;K = 𝐸[(𝑅&lt; − 𝑅A&lt; ) &times; I𝑅K − 𝑅AK L]
Correlation:
𝐶𝑜𝑟𝑟I𝑅&lt; , 𝑅K L = 𝜌&lt;K =
𝜎&lt;K
𝜎&lt; &times; 𝜎K
Portfolio analysis
Expected return of a portfolio p consisting of N assets where wi is the weight of i-th
asset in the portfolio:
C
𝐸I𝑅P L = % 𝑤&lt; &times; 𝐸(𝑅&lt; )
&lt;./
Variance of the portfolio p:
C
C
C
C
𝜎P? = % % 𝑤&lt; 𝑤K 𝜎&lt;K = % 𝑤&lt;? 𝜎&lt;? + % 𝑤&lt; 𝑤K 𝜎&lt;K
&lt;./ K./
𝛽&lt; =
&lt;./
&lt;./
K./
&lt;RK
𝐶𝑜𝑣(𝑅&lt; , 𝑅T )
𝑉𝑎𝑟(𝑅T )
Capital Asset Pricing Model
𝐸 (𝑅&lt; ) = 𝑟U + 𝛽&lt; &times; (𝐸 (𝑅T ) − 𝑟U )
Weighted average cost of capital
𝑅VWXX =
𝐸
𝐷
&times; 𝑅Y +
&times; 𝑅Z &times; (1 − 𝑇X )
𝐸+𝐷
𝐸+𝐷
10
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```