I need to calculate semi-accurately the Probability of the BOC Cutting/Hiking their Policy Rate. The end result is to get a Probability Distribution for each BOC meeting like the Federal Reserve’s FedWatch Tool. I say Semi-accurately as minor deviations are okay, just not if there’s huge differences in the probabilities calculated from both approaches.
Does anyone know how to Create this formula in Excel/Google Sheets for me? I can give Eligible hours toward the 4000 hour CFA Charterholder requirement and some compensation for a few hours or your time.
In both cases, you’ve got a formula r_{i}=\frac{365}{t_{a}+t_{b}}\left[\left(1+\frac{r_{0}}{365}\right)^{t_{a}}\left(1+\frac{Pr_{1}}{365}+\frac{(1-P)r_{0}}{365}\right)^{t_{b}}-1\right]
where r_i is implied rate =1-\frac{\textrm{futures price}}{100} r_0 is current rate and r_1 is expected rate t_a is number of days from start of period to announcement and t_b is number of days from announcement to end of period P is probability of change from r_0 to r_1 which is what you want to solve for.
Solving P=\frac{365}{r_1-r_0}\left[\frac{\left(1+\frac{r_i\left(t_a+t_b\right)}{365}\right)^{1/t_b}} {\left(1+\frac{r_0}{365}\right)^{t_a/t_b}}
-1-\frac{r_0}{365}\right]
There are 8 scheduled announcements in 2025
January 29, March 12, April 16, June 4, July 30, September 17, October 29, December 10
There are 2 futures contracts mentioned: quarterly and monthly.
As to which contract is the best, I should clarify:
the announcement date has to lie within the lifetime of the futures contract.
That tells you which contract you have to use.
Today is April 25th. Two futures contracts are available:
monthly expiring at the end of April.
quarterly expiring at the end of June.
The timing of the next announcement tells you which futures contract you have to use.
If the next announcement lies between today and the end of April, you can use either the monthly (April) or quarterly futures.
If the next announcement lies between end of April and the end of June, you use the quarterly futures.
If the next announcement lies after the end of June, you can use neither.
If today were the 25th of June, the answer would be slightly different, because now the monthly and quarterly futures are both expiring at the end of June so for the purposes of your project have become one and the same.
For the January, April, July, and October announcements, I would use the monthly futures, because there is a second announcement towards the end of each quarter which would make the use of the quarterly futures more complicated.
Why neither use Monthly or Quarterly for Meeting Dates after June? I would have to use something.
Can you clarify exactly what futures contracts are available?
Based on the Montreal Exchange links you posted, I’m under the impression that there are:
4 x quarterly futures, 1 for each quarter
12 x monthly futures, 1 for each month.
for the quarterly futures
Reference Quarter for CORRA futures contracts are based on International Monetary Market (IMM)
dates. For a given contract, interval from (and including) the 3rd Wednesday of the Contract
Reference Month, to (and not including) the 3rd Wednesday of the Delivery Month.
for the monthly contracts
The calculation period for a contract month is from, and including, the first Business Day in the
relevant contract month up to, and excluding, the first Business Day in the next calendar month.
Weekend and holiday rates are considered to be the rate applicable on the previous business day for
which a rate was reported. For example, Friday’s rate is used for Saturday and Sunday rates.
Holidays are determined based on Canadian Banks holiday (Toronto) calendar
For 2025, the quarters would be
Weds 18 Dec 2024 to Tues 18 March 2025
Weds 19 March 2025 to Tues 17 June 2025
Weds 18 June 2025 to Tues 16 Sept 2025
Weds 17 Sept 2025 to Tues 16 Dec 2025
Weds 17 Dec 2025 to Tues 21 Jan 2026
Unless there are other contracts you haven’t told us about, it’s not clear to me for example which futures contract you’d use between 5th June 2025 and 17th June 2025.
The announcement on June 4 2025 has already taken place and the next announcement is July 30 2025. The quarterly contract will expire on 17 June 2025 and the monthly contract will expire at the end of June 2025. According to the formulas on the Montreal Exchange website, neither of these 2 contracts should be affected by the decision at the July 30 2025.
The next quarterly contract will not be available until 18 June 2025 and the next monthly contract will not available until the start of July 2025.
Unless I’m missing something or there are contracts you haven’t told us about, I don’t see which contracts you can use between those 2 dates (5th June 2025 and 17th June 2025).
A solid way is to look at overnight index swaps (OIS) — they reflect market expectations pretty clearly. Add in some economist forecasts and BoC statements for context, and you’ve got a pretty good read.
