How to calculate peak-valley drawdown with SQL Server 2012? - sql-server

Question

I'm wondering if some of the new SQL Server 2012 functions would help with this problem. Here's my DDL and sample data
CREATE TABLE [dbo].[transactions]
(
[transactionId] [int] NOT NULL,
[dt] [datetime] NOT NULL,
[balance] [decimal](22, 6) NULL
);
GO
INSERT [dbo].[transactions] ([transactionId], [dt], [balance]) VALUES
(174, CAST(0x0000A19600000000 AS DateTime), CAST(1000.000000 AS Decimal(22, 6))),
(178, CAST(0x0000A19700869520 AS DateTime), CAST(1100.000000 AS Decimal(22, 6))),
(179, CAST(0x0000A19700933780 AS DateTime), CAST(1212.000000 AS Decimal(22, 6))),
(180, CAST(0x0000A19700B4B9A0 AS DateTime), CAST(1342.000000 AS Decimal(22, 6))),
(181, CAST(0x0000A19700BB0AD0 AS DateTime), CAST(1198.000000 AS Decimal(22, 6))),
(182, CAST(0x0000A19700E67030 AS DateTime), CAST(1234.000000 AS Decimal(22, 6))),
(183, CAST(0x0000A19700F358E0 AS DateTime), CAST(900.000000 AS Decimal(22, 6))),
(184, CAST(0x0000A19700F58B60 AS DateTime), CAST(876.000000 AS Decimal(22, 6))),
(185, CAST(0x0000A19700F9AA10 AS DateTime), CAST(889.000000 AS Decimal(22, 6))),
(186, CAST(0x0000A19701034700 AS DateTime), CAST(1133.000000 AS Decimal(22, 6))),
(187, CAST(0x0000A19A0089E0E0 AS DateTime), CAST(1400.000000 AS Decimal(22, 6))),
(191, CAST(0x0000A19A009450C0 AS DateTime), CAST(1566.000000 AS Decimal(22, 6))),
(192, CAST(0x0000A19A00A5E4C0 AS DateTime), CAST(1800.000000 AS Decimal(22, 6))),
(188, CAST(0x0000A19A00AA49C0 AS DateTime), CAST(1900.000000 AS Decimal(22, 6))),
(189, CAST(0x0000A19A00B54640 AS DateTime), CAST(1456.000000 AS Decimal(22, 6))),
(190, CAST(0x0000A19A00CAB2A0 AS DateTime), CAST(1234.000000 AS Decimal(22, 6))),
(193, CAST(0x0000A19A00F12660 AS DateTime), CAST(1400.000000 AS Decimal(22, 6))),
(195, CAST(0x0000A19A010087E0 AS DateTime), CAST(1444.000000 AS Decimal(22, 6))),
(196, CAST(0x0000A19E00C7F380 AS DateTime), CAST(1556.000000 AS Decimal(22, 6))),
(197, CAST(0x0000A19E00FE5560 AS DateTime), CAST(1975.000000 AS Decimal(22, 6)));
I am after the largest percentage peak-valley drawdown of the balance for the series, ordered by dt. The peak to valley drawdown is the greatest percent change in a high in the balance to the lowest low before the previous high is crossed. Better described here http://www.investopedia.com/terms/p/peak-to-valley-drawdown.asp In this data set we have two drawdowns.
First one is from 1342.00 to 876.00 (-34.72%) and the second one from 1900 to 1234 (-35.05%)
The biggest peak to valley percent drawdown in this set therefore, is -35.05%. I need a SQL Server query that can provide this value. Would rather not have to use temp tables if possible. Any ideas?

Answer 1

I don't know that any SQL Server 2012 functionality will get this value any more succinctly or efficiently than this:
;WITH x AS
(
SELECT [drop] = ((s.balance-e.balance)*100.0/s.balance)
FROM dbo.transactions AS s
INNER JOIN dbo.transactions AS e
ON s.transactionId < e.transactionId
AND s.balance > e.balance
)
SELECT [Largest Drawdown] = -MAX([drop]) FROM x;
Result:
Largest Drawdown
----------------
-35.05263157894
I do confess, though, that this works for your sample data only because your valleys are convenient for the problem you want to solve. If you change the 4th-last row to 875 this query considers that a part of the set. In other words, I've calculated drawdown here for the entire range, rather than just the range until the high is crossed again.
I suspect there is a better way to solve this query using gap/island techniques and I will try to return to it when I can focus on it adequately.

Answer 2

This will miss if the first entry is a peak
;with trnsCTE (ID,bal) AS
( -- get seqential ID
SELECT ROW_NUMBER() OVER (ORDER BY DT) as ID, [balance]
from [transactions]
),
trnsCTE2 (ID,bal) AS
( -- any peaks
select t2.ID, t2.bal
from trnsCTE as T1
join trnsCTE as T2
on ( t2.ID = t1.ID+1
and t2.bal > t1.bal )
join trnsCTE as T3
on t3.ID = t2.ID+1
and t3.bal < t1.bal
)
,
trnsCTE3 (ID,bal) AS
( -- get first peak and then bigger peaks only
SELECT distinct T1.ID, T1.BAL
from trnsCTE2 as T1
where T1.ID = (select min(ID) from trnsCTE2)
or T1.bal > (select max(bal) from trnsCTE2 where trnsCTE2.ID < t1.ID)
)
-- calculate
select t1.id, t1.bal, min(trnsCTE.bal), (t1.bal - min(trnsCTE.bal)) * 100 / t1.bal
from trnsCTE
join trnsCTE3 t1
on t1.id < trnsCTE.id
and ( trnsCTE.id < (select min(id) from trnsCTE3 where id > t1.id)
or
t1.id = ( select max(id) from trnsCTE3 ) )
group by t1.id, t1.bal
order by t1.id
This translates directly to a #temps
Did not use #temp at OP said did not want to user #temp
insert into #trnsCTE (ID,bal)
SELECT ROW_NUMBER() OVER (ORDER BY DT) as ID, [balance]
from [transactions]

Answer 3

select peak_dt, peak_balance, trough_dt, trough_balance, (peak_balance - trough_balance) * 100.0 / peak_balance as drawdown
from (
select dt as peak_dt, balance as peak_balance, nullif(last_value(dt) over (partition by peak_valley_group order by dt rows between unbounded preceding and unbounded following), dt) as trough_dt, nullif(last_value(balance) over (partition by peak_valley_group order by dt rows between unbounded preceding and unbounded following), balance) as trough_balance, isPeak
from (
select *, sum(isPeak) over (order by dt) as peak_valley_group
from (
select dt, balance, (case when forward_trend = -1 then 1 else 0 end) as isPeak, max(balance) over (partition by forward_trend order by dt) as current_max_balance
from (
-- Nulls for lead/lag here produce the desired result
select *, (case when lead(balance, 1) over (order by dt) > balance then 1 else -1 end) as forward_trend, (case when lag(balance, 1) over (order by dt) > balance then 1 else -1 end) as backward_trend
from transactions
) t
where forward_trend = backward_trend
) t
where (isPeak = 1 and balance = current_max_balance)
or isPeak = 0
) t
) t
where isPeak = 1
order by peak_dt