Expense Example	Mar. 31, 2024 USD ($)
Class F Prospectus | SAAT DEFENSIVE STRATEGY FUND | SAAT DEFENSIVE STRATEGY FUND - CLASS F
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	$ 113
Expense Example, with Redemption, 3 Years	353
Expense Example, with Redemption, 5 Years	612
Expense Example, with Redemption, 10 Years	1,352
Class F Prospectus | SAAT DEFENSIVE STRATEGY ALLOCATION FUND | SAAT DEFENSIVE STRATEGY ALLOCATION FUND - CLASS F
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	95
Expense Example, with Redemption, 3 Years	296
Expense Example, with Redemption, 5 Years	515
Expense Example, with Redemption, 10 Years	1,143
Class F Prospectus | SAAT CONSERVATIVE STRATEGY FUND | SAAT CONSERVATIVE STRATEGY FUND - CLASS F
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	122
Expense Example, with Redemption, 3 Years	381
Expense Example, with Redemption, 5 Years	660
Expense Example, with Redemption, 10 Years	1,455
Class F Prospectus | SAAT CONSERVATIVE STRATEGY ALLOCATION FUND | SAAT CONSERVATIVE STRATEGY ALLOCATION FUND - CLASS F
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	126
Expense Example, with Redemption, 3 Years	393
Expense Example, with Redemption, 5 Years	681
Expense Example, with Redemption, 10 Years	1,500
Class F Prospectus | SAAT MODERATE STRATEGY FUND | SAAT MODERATE STRATEGY FUND - CLASS F
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	133
Expense Example, with Redemption, 3 Years	415
Expense Example, with Redemption, 5 Years	718
Expense Example, with Redemption, 10 Years	1,579
Class F Prospectus | SAAT MODERATE STRATEGY ALLOCATION FUND | SAAT MODERATE STRATEGY ALLOCATION FUND - CLASS F
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	126
Expense Example, with Redemption, 3 Years	393
Expense Example, with Redemption, 5 Years	681
Expense Example, with Redemption, 10 Years	1,500
Class F Prospectus | SAAT AGGRESSIVE STRATEGY FUND | SAAT AGGRESSIVE STRATEGY FUND - CLASS F
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	138
Expense Example, with Redemption, 3 Years	431
Expense Example, with Redemption, 5 Years	745
Expense Example, with Redemption, 10 Years	1,635
Class F Prospectus | SAAT TAX-MANAGED AGGRESSIVE STRATEGY FUND | SAAT TAX-MANAGED AGGRESSIVE STRATEGY FUND - CLASS F
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	142
Expense Example, with Redemption, 3 Years	440
Expense Example, with Redemption, 5 Years	761
Expense Example, with Redemption, 10 Years	1,669
Class F Prospectus | SAAT CORE MARKET STRATEGY FUND | SAAT CORE MARKET STRATEGY FUND - CLASS F
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	143
Expense Example, with Redemption, 3 Years	443
Expense Example, with Redemption, 5 Years	766
Expense Example, with Redemption, 10 Years	1,680
Class F Prospectus | SAAT CORE MARKET STRATEGY ALLOCATION FUND | SAAT CORE MARKET STRATEGY ALLOCATION FUND - CLASS F
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	140
Expense Example, with Redemption, 3 Years	437
Expense Example, with Redemption, 5 Years	755
Expense Example, with Redemption, 10 Years	1,657
Class F Prospectus | SAAT MARKET GROWTH STRATEGY FUND | SAAT MARKET GROWTH STRATEGY FUND - CLASS F
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	146
Expense Example, with Redemption, 3 Years	452
Expense Example, with Redemption, 5 Years	782
Expense Example, with Redemption, 10 Years	1,713
Class F Prospectus | SAAT MARKET GROWTH STRATEGY ALLOCATION FUND | SAAT MARKET GROWTH STRATEGY ALLOCATION FUND - CLASS F
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	140
Expense Example, with Redemption, 3 Years	437
Expense Example, with Redemption, 5 Years	755
Expense Example, with Redemption, 10 Years	1,657
Class D Prospectus | SAAT DEFENSIVE STRATEGY FUND | SAAT DEFENSIVE STRATEGY FUND - CLASS D
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	189
Expense Example, with Redemption, 3 Years	585
Expense Example, with Redemption, 5 Years	1,006
Expense Example, with Redemption, 10 Years	2,180
Class D Prospectus | SAAT CONSERVATIVE STRATEGY FUND | SAAT CONSERVATIVE STRATEGY FUND - CLASS D
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	198
Expense Example, with Redemption, 3 Years	612
Expense Example, with Redemption, 5 Years	1,052
Expense Example, with Redemption, 10 Years	2,275
Class D Prospectus | SAAT MODERATE STRATEGY FUND | SAAT MODERATE STRATEGY FUND - CLASS D
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	210
Expense Example, with Redemption, 3 Years	649
Expense Example, with Redemption, 5 Years	1,114
Expense Example, with Redemption, 10 Years	2,400
Class D Prospectus | SAAT AGGRESSIVE STRATEGY FUND | SAAT AGGRESSIVE STRATEGY FUND - CLASS D
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	214
Expense Example, with Redemption, 3 Years	661
Expense Example, with Redemption, 5 Years	1,134
Expense Example, with Redemption, 10 Years	2,441
Class D Prospectus | SAAT CORE MARKET STRATEGY FUND | SAAT CORE MARKET STRATEGY FUND - CLASS D
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	218
Expense Example, with Redemption, 3 Years	673
Expense Example, with Redemption, 5 Years	1,154
Expense Example, with Redemption, 10 Years	2,483
Class D Prospectus | SAAT MARKET GROWTH STRATEGY FUND | SAAT MARKET GROWTH STRATEGY FUND - CLASS D
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	220
Expense Example, with Redemption, 3 Years	679
Expense Example, with Redemption, 5 Years	1,164
Expense Example, with Redemption, 10 Years	2,503
Class I Prospectus | SAAT DEFENSIVE STRATEGY FUND | SAAT DEFENSIVE STRATEGY FUND - CLASS I
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	138
Expense Example, with Redemption, 3 Years	431
Expense Example, with Redemption, 5 Years	745
Expense Example, with Redemption, 10 Years	1,635
Class I Prospectus | SAAT CONSERVATIVE STRATEGY FUND | SAAT CONSERVATIVE STRATEGY FUND - CLASS I
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	148
Expense Example, with Redemption, 3 Years	459
Expense Example, with Redemption, 5 Years	792
Expense Example, with Redemption, 10 Years	1,735
Class I Prospectus | SAAT MODERATE STRATEGY FUND | SAAT MODERATE STRATEGY FUND - CLASS I
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	160
Expense Example, with Redemption, 3 Years	496
Expense Example, with Redemption, 5 Years	855
Expense Example, with Redemption, 10 Years	1,867
Class I Prospectus | SAAT AGGRESSIVE STRATEGY FUND | SAAT AGGRESSIVE STRATEGY FUND - CLASS I
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	164
Expense Example, with Redemption, 3 Years	508
Expense Example, with Redemption, 5 Years	876
Expense Example, with Redemption, 10 Years	1,911
Class I Prospectus | SAAT CORE MARKET STRATEGY FUND | SAAT CORE MARKET STRATEGY FUND - CLASS I
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	168
Expense Example, with Redemption, 3 Years	520
Expense Example, with Redemption, 5 Years	897
Expense Example, with Redemption, 10 Years	1,955
Class I Prospectus | SAAT MARKET GROWTH STRATEGY FUND | SAAT MARKET GROWTH STRATEGY FUND - CLASS I
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	171
Expense Example, with Redemption, 3 Years	530
Expense Example, with Redemption, 5 Years	913
Expense Example, with Redemption, 10 Years	$ 1,987