# Key formulas

```Key Formulas
Present value of a cash flow stream
-
ππ# = %
'./
πΆ'
(1 + π )'
Future value of a cash flow P0 at date t
πΉπ = ππ# &times; (1 + π)'
Present value of a perpetuity starting in date 1
ππ# =
πΆ/
π
Present value of an annuity starting in date 1
ππ# =
πΆ/
1
&times; 21 −
4
(1 + π )π
Present value of a constantly growing perpetuity starting in date 1
ππ# =
πΆ/
π−π
Present value of a growing annuity starting in date 1
ππ# =
πΆ/
1+π &times; 61 − 7
8 9
π−π
1+π
9
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Measures of risk for individual assets
Variance:
C
πππ (π&lt; ) = π&lt;? = πΈ (π&lt; − πA)? = % π&lt; &times; (π&lt; − πA )?
&lt;./
Standard deviation (volatility):
ππ· (π&lt; ) = π&lt; = Fπ&lt;?
Covariance:
πΆππ£Iπ&lt; , πK L = π&lt;K = πΈ[(π&lt; − πA&lt; ) &times; IπK − πAK L]
Correlation:
πΆπππIπ&lt; , πK L = π&lt;K =
π&lt;K
π&lt; &times; πK
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
πΈIπP L = % π€&lt; &times; πΈ(π&lt; )
&lt;./
Variance of the portfolio p:
C
C
C
C
πP? = % % π€&lt; π€K π&lt;K = % π€&lt;? π&lt;? + % π€&lt; π€K π&lt;K
&lt;./ K./
π½&lt; =
&lt;./
&lt;./
K./
&lt;RK
πΆππ£(π&lt; , πT )
πππ(πT )
Capital Asset Pricing Model
πΈ (π&lt; ) = πU + π½&lt; &times; (πΈ (πT ) − πU )
Weighted average cost of capital
πVWXX =
πΈ
π·
&times; πY +
&times; πZ &times; (1 − πX )
πΈ+π·
πΈ+π·
10
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```