S&P 500 Index
The S&P 500 is widely regarded as the best single gauge of large-cap U.S. equities. According to our Annual Survey of Assets, an estimated USD 15.6 trillion is indexed or benchmarked to the index, with indexed assets comprising approximately USD 7.1 trillion of this total (as of Dec. 31, 2021). The index includes 500 leading companies and covers approximately 80% of available market capitalization.
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 22.09% per annum.
- S&P 500 Index at the close of May 17, 2024 was 5,303.27 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 42.83% per annum.
- S&P 500 Index at the close of May 17, 2024 was inside the secondary price channel.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of S&P 500 Index
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: September 21, 2022
End date: May 17, 2024
a = 7.5479
b = 0.0005
s = 0.0308
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0005) – 1
= 22.09%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0308) – 1
= 13.12%
September 21, 2022 calculations
Top border of price channel:
Exp(Y842)
= Exp(a + b × X842 + 2 × s)
= Exp(a + b × 1,220 + 2 × s)
= Exp(7.5479 + 0.0005 × 1,220 + 2 × 0.0308)
= Exp(8.2766)
= 3,930.78
Bottom border of price channel:
Exp(Y842)
= Exp(a + b × X842 – 2 × s)
= Exp(a + b × 1,220 – 2 × s)
= Exp(7.5479 + 0.0005 × 1,220 – 2 × 0.0308)
= Exp(8.1533)
= 3,474.99
May 17, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(7.5479 + 0.0005 × 1,824 + 2 × 0.0308)
= Exp(8.6068)
= 5,468.90
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(7.5479 + 0.0005 × 1,824 – 2 × 0.0308)
= Exp(8.4836)
= 4,834.76
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 22.09% per annum.
- S&P 500 Index at the close of May 17, 2024 was 5,303.27 and was inside the primary price channel.
Secondary Trend
Start date: September 21, 2023
End date: May 17, 2024
a = 6.8075
b = 0.0010
s = 0.0229
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0010) – 1
= 42.83%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0229) – 1
= 9.57%
September 21, 2023 calculations
Top border of price channel:
Exp(Y1,093)
= Exp(a + b × X1,093 + 2 × s)
= Exp(a + b × 1,585 + 2 × s)
= Exp(6.8075 + 0.0010 × 1,585 + 2 × 0.0229)
= Exp(8.4012)
= 4,452.36
Bottom border of price channel:
Exp(Y1,093)
= Exp(a + b × X1,093 – 2 × s)
= Exp(a + b × 1,585 – 2 × s)
= Exp(6.8075 + 0.0010 × 1,585 – 2 × 0.0229)
= Exp(8.3098)
= 4,063.39
May 17, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(6.8075 + 0.0010 × 1,824 + 2 × 0.0229)
= Exp(8.6346)
= 5,622.94
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(6.8075 + 0.0010 × 1,824 – 2 × 0.0229)
= Exp(8.5432)
= 5,131.71
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 42.83% per annum.
- S&P 500 Index at the close of May 17, 2024 was inside the secondary price channel.