Sharpe Ratio

[sharriss]

Hello,

I've been paper trading for a short while now and I'm wanting to analyse my trades.

I have them all stored in a spreadsheet and I'm currently mapping the Equity Curve, ROCE, Average Profit/Loss etc

I've been looking at the Sharpe Ratio and I've tried to add it to my spreadsheet but I'm having a few problems, can anyone help?

My understanding of the Sharpe Ratio is as follows...

S = (r - R) / SD

Where
S = Sharpe Ratio
r = Annual Equity Return (%)
R = Risk Free Return (say 5%)
SD = Standard Deviation of Return

So assuming I have figures as follows (entirely made up)

Date Equity Weekly Return
01/12/2004 £10,000 0
08/12/2004 £10,025 0.25%
15/12/2004 £10,089 0.64%
22/12/2004 £9,956 -1.32%
29/12/2004 £10,128 1.73%
05/12/2004 £10,125 -0.03%
12/01/2005 £10,184 0.58%
19/01/2005 £10,194 0.10%
26/01/2005 £10,275 0.79%
02/02/2005 £10,389 1.11%
09/02/2005 £10,451 0.60%
16/02/2005 £10,486 0.33%
23/02/2005 £10,515 0.29%
02/03/2005 £10,642 1.20%

I have an Equity Return of £642 over 13 weeks (i.e. 10,642 - 10,000).
This means a Weekly Equity Return of £49.38 (i.e. 642/13) or 0.49%
Multiply this by 52 weeks in the year and I get 25.68% Annual Equity return.

The Standard Deviation of my Weekly Return %'ages is 0.007 (i.e. STDEVP(0.25, 0.64, -1.32 ... 1.20)).
0.007 * SQRT(52) = 0.0505 Annual Standard Deviation.

Therefore my Sharpe Ratio is...

(25.68 - 5) / 0.0505 = 4.0977

Is this right?

 

[Chagi]

A few things here. Please don't take any of the following personally, just providing an honest answer. First, the formula you have for Sharpe's Measure (ratio) is correct, since it is:

S = (Expected Return "risky" investment - Risk Free Return) / Std. Dev. of the "risky" investment

The second important thing to note is that your annual return calculation is incorrect, since it is not correct to simply multiple your average weekly percentage return by the number of weeks in a year - you are essentially ignoring compounding (assuming that you are reinvesting your gains). If you are achieving a certain percentage of weekly (daily, monthly, whatever) return, the dollar returns will increase over time due to compounding, they won't remain linear.

For example, using your numbers, your annual return would be approx 28.94%.

With regards to calculting standard deviation, I may be wrong about this, but I'm not sure why you are doing something to standard dev. in order to get annual standard dev.? If the standard deviation of your sample is 0.007, and you are assuming your returns to be constant, then your standard dev. should be assumed to be constant as well (even though both expectations are likely to be unrealistic in the real world). I don't think that there is such a calculation as "annual standard deviation" - standard deviation is just a statistical measure of a sample that is assumed to be normally distributed.

Also, I should point out that I believe you calculated your standard deviation incorrectly. It seemed very low to me (since your average return is 0.447857), so I calculated it with Excel =STDEV(range), and I got 0.712300483.

Keeping in mind that I don't believe it is correct to assume standard dev. to be constant over the entire year, your Sharpe ratio for one week would be:

S = (.0048 - .00096) / 0.007123
S = 0.5390

 

[sharriss]

Thanks Chagi,

What I posted was my understanding of the Sharpe Ratio that I had got from various different websites. There was quite a lot of conflicting information along side some not very well explained information, so I had to guess some of it.

Thanks for the help, I'll make some adjustments.

Does anyone else have a good understanding of the Sharpe Ratio and how to calculate it?

Thanks,

 

[Chagi]

Thanks Chagi,

What I posted was my understanding of the Sharpe Ratio that I had got from various different websites. There was quite a lot of conflicting information along side some not very well explained information, so I had to guess some of it.

Thanks for the help, I'll make some adjustments.

Does anyone else have a good understanding of the Sharpe Ratio and how to calculate it?

Thanks,

No problem.

The formula for the reward to variability (Sharpe's) ratio is correct, just a matter of plugging in the right numbers, we studied it briefly last semester in my portfolio management class, so let me know if you have any further questions.

 

[the blades]

Thanks Chagi,

What I posted was my understanding of the Sharpe Ratio that I had got from various different websites. There was quite a lot of conflicting information along side some not very well explained information, so I had to guess some of it.

Thanks for the help, I'll make some adjustments.

Does anyone else have a good understanding of the Sharpe Ratio and how to calculate it?

Thanks,

I think you need clarification on the annual STDEV.

You are multiplying the weekly SD by sqrt(52). If you were to take samples, 52 in size, from a larger population, then the averages of the samples would form a population with a standard deviation of that of the larger population, divided by SQRT(52). You are effectively reversing this and I believe there is some merit in this...I just wish I could remember clearly - it must be the effect of beer

Any real stats experts out there?

UTB

 

[Chagi]

I think you need clarification on the annual STDEV.

You are multiplying the weekly SD by sqrt(52). If you were to take samples, 52 in size, from a larger population, then the averages of the samples would form a population with a standard deviation of that of the larger population, divided by SQRT(52). You are effectively reversing this and I believe there is some merit in this...I just wish I could remember clearly - it must be the effect of beer

Any real stats experts out there?

UTB

I won't call myself a stats "expert", but I have completed three university level stats courses so far for my business degree, so I have managed to retain a few things in my noggin along the way.

The only way that I have ever covered for calculating standard deviation and variance is to plug in all of the numbers for a sample or population. I think it's more likely for his standard deviation to be much larger on annual basis than it is to get smaller. I would speculate that annual standard dev for a rate of return of 29% would probably easily be 10-15% or higher - usually high rates of returns are tied to high risk (volatility).

 

[sharriss]

Thanks for the replies so far, but I'm not much closer to fully understanding how to calculate and use the Sharpe Ratio.

There's so much information on the Internet but I still haven't found a detailed working example.

I know the formula and what it tells you about your trades but not how to use my data to calculate a meaningful figure.

Is there nobody out there who can either explain it or point me in the right direction to some detailed information with a simple working example?

 

[theknifemac]

I think that taking the weekly std dev and multiplying by sqrt(52) is correct. I think the Sharpe ratio should be calculated as follows:

Calc std dev of returns

Annualise these by multiply by sqrt(52)

Calculate annualised returns = avg(weekly returns) * 52

Then calculate the sharpe ratio. I would also think the riskfree rate should be a bit lower than 5%.

Hope this helps

Stew

 

[DIN]

sharpe ratio

Thanks for the replies so far, but I'm not much closer to fully understanding how to calculate and use the Sharpe Ratio.

There's so much information on the Internet but I still haven't found a detailed working example.

I know the formula and what it tells you about your trades but not how to use my data to calculate a meaningful figure.

Is there nobody out there who can either explain it or point me in the right direction to some detailed information with a simple working example?

sharriss,

1) you cannot and should not take 13 weeks and compound it to 52. The number will be meaninless. either wait until there are 52 observations for weekly, 12 for monthly or 260 for daily.

It is an expost calc not ex ante, ie, it is not predictive so you cannot assume what happened in the 1st 13 weeks will happen for the rest of the year, maybe thats is another topic

2) don't get standard dev mixed up with volatility. for the sharp ratio you need to know what the
vol is rather than the sd. formula is: SQRT(52)*STDEV(list of your returns) pref log returns but
doesn't make much diff.

check this out below, for the purposes of the calc, I'm assuming / pretending that you traded thru your fictional year and prodcued the values listed below, just so you can see where the numbers come from.

hope it helps.for what its worth, I think this is one of the best measures to determine your worth as a trader.


week Values Return
1 10000
2 10025 0.250
3 10089 0.638
4 9956 -1.318
5 10128 1.728
6 10125 -0.030
7 10184 0.583
8 10194 0.098
9 10257 0.618
10 10389 1.287
11 10451 0.597
12 10486 0.335
13 10515 0.277
14 10642 1.208
15 10000 -6.033
16 10025 0.250
17 10089 0.638
18 9956 -1.318
19 10128 1.728
20 10125 -0.030
21 10184 0.583
22 10194 0.098
23 10257 0.618
24 10389 1.287
25 10451 0.597
26 10486 0.335
27 10515 0.277
28 10642 1.208
29 10000 -6.033
30 10025 0.250
31 10089 0.638
32 9956 -1.318
33 10128 1.728
34 10125 -0.030
35 10184 0.583
36 10194 0.098
37 10257 0.618
38 10389 1.287
39 10451 0.597
40 10486 0.335
41 10515 0.277
42 10642 1.208
43 10000 -6.033
44 10025 0.250
45 10089 0.638
46 9956 -1.318
47 10128 1.728
48 10125 -0.030
49 10184 0.583
50 10194 0.098
51 10257 0.618
10389 1.287

Volatility 12.28451589 SQRT(52)*STDEV(list of returns)

Total Return 3.89 ((10389/10000)-1)*100
Total RFR (cash) 5.00 your fig
Diff -1.11

Sharp Ratio -0.09 Vol / Diff


hope this helps

D

 

[DIN]

sharpe ratio

Thanks for the replies so far, but I'm not much closer to fully understanding how to calculate and use the Sharpe Ratio.

There's so much information on the Internet but I still haven't found a detailed working example.

I know the formula and what it tells you about your trades but not how to use my data to calculate a meaningful figure.

Is there nobody out there who can either explain it or point me in the right direction to some detailed information with a simple working example?

sharriss,

Some pointers....

1) you cannot and should not take 13 weeks and compound it to 52. The number will be meaningless. either wait until there are 52 observations for weekly, 12 for monthly or 260 for daily.

It is an expost calc not ex ante, ie, it is not predictive so you cannot assume what happened in the 1st 13 weeks will happen for the rest of the year, maybe that is is another topic

2) don't get standard dev mixed up with volatility. for the sharp ratio you need to know what the
vol is rather than the SD. formula is: SQRT(52)*STDEV(list of your returns) pref erably log returns but doesn't make much diff.

check this out below, for the purposes of the calc, I'm assuming / pretending that you traded thru your fictional year and prodcued the values listed below, just so you can see where the numbers come from.

.for what its worth, I think this is one of the best measures to determine your worth as a trader.


week Values Return
1 10000
2 10025 0.250
3 10089 0.638
4 9956 -1.318
5 10128 1.728
6 10125 -0.030
7 10184 0.583
8 10194 0.098
9 10257 0.618
10 10389 1.287
11 10451 0.597
12 10486 0.335
13 10515 0.277
14 10642 1.208
15 10000 -6.033
16 10025 0.250
17 10089 0.638
18 9956 -1.318
19 10128 1.728
20 10125 -0.030
21 10184 0.583
22 10194 0.098
23 10257 0.618
24 10389 1.287
25 10451 0.597
26 10486 0.335
27 10515 0.277
28 10642 1.208
29 10000 -6.033
30 10025 0.250
31 10089 0.638
32 9956 -1.318
33 10128 1.728
34 10125 -0.030
35 10184 0.583
36 10194 0.098
37 10257 0.618
38 10389 1.287
39 10451 0.597
40 10486 0.335
41 10515 0.277
42 10642 1.208
43 10000 -6.033
44 10025 0.250
45 10089 0.638
46 9956 -1.318
47 10128 1.728
48 10125 -0.030
49 10184 0.583
50 10194 0.098
51 10257 0.618
52 10389 1.287

Volatility 12.28451589 SQRT(52)*STDEV(list of returns)

Total Return 3.89 ((10389/10000)-1)*100
Total RFR (cash) 5.00 your fig
Diff -1.11

Sharp Ratio -0.09 Vol / Diff


hope this helps

D

 

[DIN]

sharpe ratio

Thanks for the replies so far, but I'm not much closer to fully understanding how to calculate and use the Sharpe Ratio.

There's so much information on the Internet but I still haven't found a detailed working example.

I know the formula and what it tells you about your trades but not how to use my data to calculate a meaningful figure.

Is there nobody out there who can either explain it or point me in the right direction to some detailed information with a simple working example?

sharriss,

Some pointers....

1) you cannot and should not take 13 weeks and compound it to 52. The number will be meaningless. either wait until there are 52 observations for weekly, 12 for monthly or 260 for daily.

It is an expost calc not ex ante, ie, it is not predictive so you cannot assume what happened in the 1st 13 weeks will happen for the rest of the year, maybe that is is another topic

2) don't get standard dev mixed up with volatility. for the sharp ratio you need to know what the
vol is rather than the SD. formula is: SQRT(52)*STDEV(list of your returns) pref erably log returns but doesn't make much diff.

check this out below, for the purposes of the calc, I'm assuming / pretending that you traded thru your fictional year and prodcued the values listed below, just so you can see where the numbers come from.

.for what its worth, I think this is one of the best measures to determine your worth as a trader.
It values your returns against cash in relation to the volatility of those returns, if you have underperformed vs cah then it will always be negative.

week Values Return
1 10000
2 10025 0.250
3 10089 0.638
4 9956 -1.318
5 10128 1.728
6 10125 -0.030
7 10184 0.583
8 10194 0.098
9 10257 0.618
10 10389 1.287
11 10451 0.597
12 10486 0.335
13 10515 0.277
14 10642 1.208
15 10000 -6.033
16 10025 0.250
17 10089 0.638
18 9956 -1.318
19 10128 1.728
20 10125 -0.030
21 10184 0.583
22 10194 0.098
23 10257 0.618
24 10389 1.287
25 10451 0.597
26 10486 0.335
27 10515 0.277
28 10642 1.208
29 10000 -6.033
30 10025 0.250
31 10089 0.638
32 9956 -1.318
33 10128 1.728
34 10125 -0.030
35 10184 0.583
36 10194 0.098
37 10257 0.618
38 10389 1.287
39 10451 0.597
40 10486 0.335
41 10515 0.277
42 10642 1.208
43 10000 -6.033
44 10025 0.250
45 10089 0.638
46 9956 -1.318
47 10128 1.728
48 10125 -0.030
49 10184 0.583
50 10194 0.098
51 10257 0.618
52 10389 1.287

Volatility 12.28% SQRT(52)*STDEV(list of returns)

Total Return 3.89 ((10389/10000)-1)*100
Total RFR (cash) 5.00 your fig
Diff -1.11

Sharp Ratio -0.09 Vol / Diff


hope this helps

D

 

[DIN]

sorry, somehow it has come out 3 times.!!!

 

[sharriss]

DIN,

I think I've got the message now!

Thanks for the reply, basically I need to get some more data - I only have 13 weeks worth so far.

So I'll keep this post and after a year look at it again and work out the calculation.

Thanks everyone for the help.