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: Bob Fulkes writes of Sharpe ratios of mechanical systems.
Attached is a ELA written by Bob Fulkes, with the function outline below. It
calculates the Sharpe Ratio as a function to be used in an indicator...to be
used in conjunction with a system. I find it to be very useful and I want to
thank Bob for it.
{Function: SharpeRatio}
{ *******************************************************************
Function : SharpeRatio
Last Edit : 11/24/98
Provided By : Bob Fulks
Description : This function calculates and returns the Sharpe Ratio
of a series of account values. It samples the series of values
on a yearly, quarterly, monthly, weekly, or daily basis as
determined by an input. It also calculates average return and
standard deviation. It prints the results in a form suitable for
importing into an Excel spreadsheet for plotting.
Inputs:
Mode - Sampling period (0=yearly, 1=quarterly, 2=monthly,
3=weekly, 4=daily
NetValue - The series of values to be sampled. It should be
equal to the beginning equity plus accumulated net profits.
Periods - The number of yearly, quarterly, etc., periods to
include in the calculation. If this value is zero, the
function will use all periods up to a maximum of 1500.
PrntMode:
zero - Print one line summary only on last bar
> zero - Print values as stored in array plus summary
< zero - Do not print anything
Futures:
TRUE - For futures trading (Sharpe = Ave / SDev)
FALSE - For Stocks (Sharpe = (Ave - 5) / SDev)
Method: The function samples the value of the trading account at
periodic intervals, calculates returns in each period, then
calculates the average and standard deviation of returns and
annualizes them. It then calculates to Sharpe Ratio as noted
above.
Assumptions: The usage for stocks assumes a constant value of 5%
for the risk-free return (T-Bill interest rate). This is a good
assumption for recent times but may be incorrect for the distant
past. The Sharpe Ratio is independent of the sampling interval
if the returns are normally distributed. Returns are typically
not strictly normally distributed so the sampling interval will
affect the results somewhat. There should be more than about 25
samples to get reasonable accuracy so use daily samples for 1
to 6 months of trades, weekly samples for 6 months to 24 months
of trades, etc.
© 1998 Robert G. Fulks, All rights reserved.
********************************************************************}
Input: Mode(NumericSimple),
{0=yearly, 1=quarterly, 2=monthly, 3=weekly, 4=daily}
NetValue(NumericSimple),
{Net value of account = Beginning Equity + NetProfit}
Periods(NumericSimple),
{Number of periods to use in calculation, zero = all}
PrntMode(NumericSimple),
{0 = print summary, 1 = include detail, -1 = don't print}
Futures(TrueFalse);
{TRUE for Futures, FALSE for Stocks}
Vars: Index(0), {Index used to index Return array}
SIndex(0), {Index used to sum Return array}
LNetVal(0), {NetValue at end of previous period}
LClose(0), {Close at end of previous period}
YClose(0), {Close at end of previous bar}
Size(0), {Sixe of data to be stored in array}
ILast(0), {Number of entries in array}
Ave(0), {Average return}
ASum(0), {Used to calc Average}
SSum(0), {Used to calc Standard Deviation}
SDev(0), {Standard Deviation}
SDMult(0), {Multiplier to annualize Standard Deviation}
Mo(0), {Month for bar}
MP(0), {MarketPosition}
MPX(0), {MarketPosition flag becomes 1 on first trade}
YMo(0), {Month for previous bar}
Yr(-99), {Year for bar}
YYr(0), {Year for previous bar}
YDate(0), {Date for previous bar}
AvMult(0), {Multiplier to annualize Average}
NetVal(0), {NetValue series}
YNetVal(0), {Netval for previous bar}
Active(FALSE), {False for first calc then true thereafter}
Record(FALSE), {Flag to trigger calculation at end of period}
Summary(FALSE), {Flag set if summary printed}
StDate(0), {Start date}
Sharpe(0); {Sharpe Ratio}
Array: Return[1500](0); {Table of returns as a percent}
Size = iff(Periods > 0, Periods, 1500);
Size = MinList(Size, 1500);
NetVal = Netvalue;
Mo = Month(Date);
Yr = Year(Date);
{This determines marketposition in either systems or indicators}
if MarketPosition <> 0 then
MP = MarketPosition
else
MP = I_MarketPosition;
MPX = iff(MP <> 0, 1, MPX);
Condition1 = Mo = 1 or Mo = 4 or Mo = 7 or Mo = 10;
begin
{Initialize for yearly}
if Mode = 0 and Yr <> YYr then begin
SDMult = 1;
AvMult = 1;
Record = TRUE;
end;
{Initialize for quarterly}
if Mode = 1 and Mo <> YMo and Condition1 then begin
SDMult = 2;
AvMult = 4;
Record = TRUE;
end;
{Initialize for monthly}
if Mode = 2 and Mo <> YMo then begin
SDMult = SquareRoot(12);
AvMult = 12;
Record = TRUE;
end;
{Initialize for weekly}
if Mode = 3 and DayOfWeek(Date) < DayOfWeek(YDate) then begin
SDMult = SquareRoot(52);
AvMult = 52;
Record = TRUE;
end;
{Initialize for daily}
if Mode = 4 and Date <> YDate then begin
SDMult = SquareRoot(253);
AvMult = 253;
Record = TRUE;
end;
end;
{Action if new year, quarter, month, week, or day}
if Record = TRUE then begin
if Active = TRUE then begin
{Each time except first time}
begin
ILast = ILast + 1;
if LNetVal <> 0 then Value1 = YNetVal / LNetVal;
if Value1 > 0 then Return[Index] = 100 * Log(Value1);
if PrntMode > 0 then Print(Index:5:0, Date:7:0, YClose:6:2,
LClose:6:2, YNetVal:7:0, LNetVal:7:0, Return[Index]:4:2);
Index = Mod(Index + 1, Size);
end;
end else
{First time only after initial position}
if MPX > 0 then begin
Active = TRUE;
StDate = Date;
if PrntMode > 0 then Print(Index:5:0, Date:7:0, YClose:6:2,
LClose:6:2, YNetVal:7:0, LNetVal:7:0, Return[Index]:4:2);
end;
LClose = YClose;
LNetVal = YNetVal;
Record = FALSE;
end;
{Calculate and print summary}
if Active = TRUE and Summary = FALSE and
(LastBarOnChart or ILast >= Size) then begin
{Calculate average return in period}
Summary = TRUE;
ASum = 0;
ILast = MinList(Size, ILast);
for SIndex = 0 to ILast - 1 begin
ASum = ASum + Return[SIndex];
end;
Ave = ASum / ILast;
{Calculate annualized standard deviation}
SSum = 0;
for SIndex = 0 to ILast - 1 begin
SSum = SSum + Square(Return[SIndex] - Ave);
end;
SDev = SDMult * SquareRoot(SSum / ILast);
{Annualize average}
Ave = AvMult * Ave;
{Convert back to ratios from logarithms}
SDev = 100 * (ExpValue(SDev / 100) - 1);
Ave = 100 * (ExpValue(Ave / 100) - 1);
{Calculate Sharpe Ratio}
if SDev <> 0 then begin
if Futures then
Sharpe = Ave / SDev
else
Sharpe = (Ave - 5) / SDev;
end;
if PrntMode >= 0 then
Print( ",", StDate:6:0, ",", ILast:6:0, ",", SDev:6:1, "%,", Ave:6:1,
"%,",
Sharpe:3:2, ", ",GetSymbolName, ",");
end;
{Print(Date:6:0, NetVal, Sharpe:4:2, MP:2:0, Active);}
YMo = Mo;
YYr = Yr;
YDate = Date;
YClose = Close;
YNetVal = NetVal;
SharpeRatio = Sharpe;
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