LO 7.6 Portfolio (2 asset) VaR

10daysANDexpected

Inputs
Notes:
Trading days /year
252
Initial portfolio value (W)
$100
VaR Time horizon (days) (h)
10
Asset returns/volatility are expressed annually, but our VaR will refer to a number of days. Selecting the time horizon is a design decision.
VaR confidence interval
95%
The other design decision is the confidence (typically 95% or 99%). VaR is not the worst case scenario; VaR is the worst loss associated with a given probability.
Asset A
Volatility (per year)
10%
Expected Return (per year)
15%
Portfolio Weight (Asset A)
50%
Asset B
Volatility
20%
Expected Return (per year)
25%
Portfolio Weight (Asset B)
50%
Correlation (A,B)
 1.00 
Outputs
Solved Annual Metrics
Covariance (A,B)
 0.0200 
Covariance = (correlation A,B)(volatility A)(volatiltiy B)
Portfolio variance
 0.0225 
The key formula for two-asset variance; please make sure you know that we can substitute the covariance with (correlation A,B)(volatility A)(volatiltiy B)
Expected portfolio return (per year)
20%
Expected return is simply weighted average expected return
Portfolio volatility (per year)
15.0%
Portfolio volatility for the two-asset portfolio
Solved Periodic (h days) Metrics
Expected periodic return (u)
0.79%
Annual return scaled by time
Standard deviation (h)
2.99%
The portfolio's annual volatiltiy scaled by the square root of time (the square root of time rule)
z-value
-1.64
95.0% of the area under a normal curve is to the right of -1.64 standard deviations. Or, 5.0% is to the left.
Expected future value
 100.79 
The portfolio value if it grows at the expected return over the period
Relative VaR
$4.91
Basic (relative) dollar VaR: portfolio scaled by volatility (itself scaled by square root of time) and scaled by confidence (critical value)
Absolute VaR
$4.12
Basic absolute dollar VaR: the loss from zero. This is less due to the expected (gain) return.

cht_10days

10days

VAR PARAMETERS
TOGGLE ANSWER WORK-OUT
Trading days /year
252
0
95% Confidence
-1.64485362695147
1
99% Confidence
-2.32634787404084
0
MODEL ASSUMPTIONS:
TO DISPLAY IN GRID:
Portfolio value(W)
$100
Expected return
0.00%
=
 = 0% x (10/252)
Expected return (per year)
0%
Std. deviation
3.16%
=
 = 16% x SQRT(10/252)
Standard deviation (per year)
15.9%
z =
1.64
Time horizon (days)
10
Absolute VAR
$5.20
=
-$100.00 x [ 0.00% + (-1.64 x 3.16%) ]
Standard deviation (h)
3.16%
0.03162277660168
Relative VAR
$5.20
-$100.00 x  (-1.64 x 3.16%)
Expected return (u)
0.00%
Confidence interval
95%
Guess (input):
z-value
-1.64
Expected Value
$100
Abs1(difference)
5.20
Evaluate Answer (is difference small enough?)
Absolute VAR
$5.20
Abs2(difference)
94.80
Relative VAR
$5.20
$94.80
Min(Abs1,Abs2)
5.20
Show
Show
Is this 
Is this 
right
left
X-axis
#N/A
delta
Z
right tail?
left tail?
(green)
(red)
-31.62
0.00%
94.0
 0.028890 
-1.90
0.00%
0.00%
94.2
 0.033318 
0.44%
-1.83
0.00%
0.44%
0.0044
94.4
 0.038291 
0.50%
-1.77
0.00%
0.50%
0.005
94.6
 0.043853 
0.56%
-1.71
0.00%
0.56%
0.0056
94.8
 0.050048 
0.62%
-1.64
0.62%
0.00%
0.0062
0.0062
95.0
95
 0.056923 
0.69%
-1.58
0.69%
0.00%
0.0069
95.2
 0.064521 
0.76%
-1.52
0.76%
0.00%
0.0076
95.4
 0.072883 
0.84%
-1.45
0.84%
0.00%
0.0084
95.6
 0.082052 
0.92%
-1.39
0.92%
0.00%
0.0092
95.8
 0.092063 
1.00%
-1.33
1.00%
0.00%
0.01
96.0
96
 0.102952 
1.09%
-1.26
1.09%
0.00%
0.0109
96.2
 0.114747 
1.18%
-1.20
1.18%
0.00%
0.0118
96.4
 0.127473 
1.27%
-1.14
1.27%
0.00%
0.0127
96.6
 0.141148 
1.37%
-1.08
1.37%
0.00%
0.0137
96.8
 0.155786 
1.46%
-1.01
1.46%
0.00%
0.0146
97.0
97
 0.171391 
1.56%
-0.95
1.56%
0.00%
0.0156
97.2
 0.187960 
1.66%
-0.89
1.66%
0.00%
0.0166
97.4
 0.205484 
1.75%
-0.82
1.75%
0.00%
0.0175
97.6
 0.223942 
1.85%
-0.76
1.85%
0.00%
0.0185
97.8
 0.243308 
1.94%
-0.70
1.94%
0.00%
0.0194
98.0
98
 0.263545 
2.02%
-0.63
2.02%
0.00%
0.0202
98.2
 0.284607 
2.11%
-0.57
2.11%
0.00%
0.0211
98.4
 0.306441 
2.18%
-0.51
2.18%
0.00%
0.0218
98.6
 0.328985 
2.25%
-0.44
2.25%
0.00%
0.0225
98.8
 0.352168 
2.32%
-0.38
2.32%
0.00%
0.0232
99.0
99
 0.375915 
2.37%
-0.32
2.37%
0.00%
0.0237
99.2
 0.400141 
2.42%
-0.25
2.42%
0.00%
0.0242
99.4
 0.424758 
2.46%
-0.19
2.46%
0.00%
0.0246
99.6
 0.449672 
2.49%
-0.13
2.49%
0.00%
0.0249
99.8
 0.474785 
2.51%
-0.06
2.51%
0.00%
0.0251
100
100
 0.500000 
2.52%
0.00
2.52%
0.00%
0.0252
100.2
 0.525215 
2.52%
0.06
2.52%
0.00%
0.0252
100.4
 0.550328 
2.51%
0.13
2.51%
0.00%
0.0251
100.6
 0.575242 
2.49%
0.19
2.49%
0.00%
0.0249
100.8
 0.599859 
2.46%
0.25
2.46%
0.00%
0.0246
101.0
101
 0.624085 
2.42%
0.32
2.42%
0.00%
0.0242
101.2
 0.647832 
2.37%
0.38
2.37%
0.00%
0.0237
101.4
 0.671015 
2.32%
0.44
2.32%
0.00%
0.0232
101.6
 0.693559 
2.25%
0.51
2.25%
0.00%
0.0225
101.8
 0.715393 
2.18%
0.57
2.18%
0.00%
0.0218
102.0
102
 0.736455 
2.11%
0.63
2.11%
0.00%
0.0211
102.2
 0.756692 
2.02%
0.70
2.02%
0.00%
0.0202
102.4
 0.776058 
1.94%
0.76
1.94%
0.00%
0.0194
102.6
 0.794516 
1.85%
0.82
1.85%
0.00%
0.0185
102.8
 0.812040 
1.75%
0.89
1.75%
0.00%
0.0175
103.0
103
 0.828609 
1.66%
0.95
1.66%
0.00%
0.0166