Returns and risk

Volatility and drawdowns

Measure risk from a price history: sample standard deviation, annualised volatility and maximum drawdown.

22 minintermediateMembers

Learning objectives

Calculate the sample standard deviation of monthly returns and annualise it
Build a running-peak drawdown series and find the maximum drawdown
Explain what volatility and drawdown each say about risk

Two shares can both return 10% a year, one gently and one through stomach-churning swings. Investors care about the path, not just the destination: a large fall can force a sale at the worst moment, and a 50% loss needs a 100% gain to recover.

Analysts summarise the path with two numbers. Volatility (the standard deviation of returns) measures how widely returns scatter around their average. Maximum drawdown measures the worst peak-to-trough fall an investor actually lived through. Bustan Foods Co. is a fictional listed food producer, and its share prices, the market index and all other figures are invented for teaching. Examples are educational and illustrative, not investment advice.

Bustan Foods Co. share price vs the market index, rebased to 100 (fictional data)Bustan share priceMarket index

Data

Month	Bustan share price	Market index
0	100	100
1	102	101
2	104	102
3	104	100
4	105	102
5	122	112
6	112	108
7	109	105
8	104	104
9	98	102
10	95	103
11	95	100
12	103	99
13	108	105
14	112	105
15	118	110
16	123	112
17	120	108
18	116	104
19	114	105
20	107	101
21	108	98
22	112	98
23	110	97
24	108	98
25	106	95
26	105	90
27	105	91
28	99	91
29	105	94
30	119	101
31	123	107
32	133	112
33	121	111
34	114	110
35	109	115
36	119	119

Included with a Formula Quest membership

The rest of this lesson is for members. Members get the full lesson, including its 4 graded exercises, and every other Finance Quest lesson.

View Formula Quest memberships Sign in

Month	Bustan share price	Market index
0	100	100
1	102	101
2	104	102
3	104	100
4	105	102
5	122	112
6	112	108
7	109	105
8	104	104
9	98	102
10	95	103
11	95	100
12	103	99
13	108	105
14	112	105
15	118	110
16	123	112
17	120	108
18	116	104
19	114	105
20	107	101
21	108	98
22	112	98
23	110	97
24	108	98
25	106	95
26	105	90
27	105	91
28	99	91
29	105	94
30	119	101
31	123	107
32	133	112
33	121	111
34	114	110
35	109	115
36	119	119

Month	Bustan share price	Market index
0	100	100
1	102	101
2	104	102
3	104	100
4	105	102
5	122	112
6	112	108
7	109	105
8	104	104
9	98	102
10	95	103
11	95	100
12	103	99
13	108	105
14	112	105
15	118	110
16	123	112
17	120	108
18	116	104
19	114	105
20	107	101
21	108	98
22	112	98
23	110	97
24	108	98
25	106	95
26	105	90
27	105	91
28	99	91
29	105	94
30	119	101
31	123	107
32	133	112
33	121	111
34	114	110
35	109	115
36	119	119

Month	Bustan share price	Market index
0	100	100
1	102	101
2	104	102
3	104	100
4	105	102
5	122	112
6	112	108
7	109	105
8	104	104
9	98	102
10	95	103
11	95	100
12	103	99
13	108	105
14	112	105
15	118	110
16	123	112
17	120	108
18	116	104
19	114	105
20	107	101
21	108	98
22	112	98
23	110	97
24	108	98
25	106	95
26	105	90
27	105	91
28	99	91
29	105	94
30	119	101
31	123	107
32	133	112
33	121	111
34	114	110
35	109	115
36	119	119