Question

Katie is reviewing his stock portfolio return from the last 5 years. He initially invested 100,000 and his annual returns were:

Year 1: 20.0%

Year 2: 5.0%

Year 3: -17.0%

Year 4: 15.5%

Year 5: 52.1%

What is Katies arithmatic average annual return?

What is Katies geometric average annual return?

What is the standard deviationof Katies returns for this 5 year period?

Answer 1

1)

No. of years	Return (in %)
1	20
2	5
3	-17
4	15.5
5	52.1
Total return	75.6

Arithmatic average annual return = Total return of all years / no.of years

= 75.6 / 5 = 15.12 %

2) Geometric average annual return = ((1 + R1) * (1 + R2 ) * (1 + R3) * (1 + R4) ........* (1+ Rn))1/n - 1

here, returns of 5 years are -

0.2

0.05

-0.17

0.155

0.521

Geometric mean = ((1 + 0.2) ( 1 + 0.05) ( 1 - 0.17) ( 1 +0.155) (1 + 0.521))1/5 - 1

solving this equation we will get,

= ( 1.837214379 )1/5 - 1

= 1.1294 - 1 (approx)

= 0.1294

= 12.94 % (approx)

3) Standard diviation

No. of years	Return (in %)	( Return - Mean return)	( Return - Mean return)2
1	20	4.88	23.8144
2	5	-10.12	102.4144
3	-17	-32.12	1031.6944
4	15.5	0.38	0.1444
5	52.1	36.98	1367.5204

= 22.47 % (approx)

Hope it helps!