^ IFA Index Portfolios Matches Expected: 50.0% {{(data.length / 2) | number:0 }} {{marketcoin ? periodLabel + ' UU+DD' : ' HH+TT'}} Observed: {{Math.round(1000 * (aboveMedianUpCoin + belowMedianDownCoin) / data.length) / 10 |number:1 }}% {{Math.round(1000 * (twoCoinsAboveMedianUpCoin + twoCoinsBelowMedianDownCoin) / data.length) / 10 |number:1 }}% {{aboveMedianUpCoin + belowMedianDownCoin | number}} {{twoCoinsAboveMedianUpCoin + twoCoinsBelowMedianDownCoin | number}} {{marketcoin ? periodLabel + ' UU+DD' : ' HH+TT'}} Mismatches Expected: 50.0% {{data.length / 2 | number:0 }} {{marketcoin ? periodLabel + ' UD+DU' : ' HT+TU'}} Observed: {{Math.round(1000 * (aboveMedianDownCoin + belowMedianUpCoin) / data.length) / 10 |number:1 }}% {{Math.round(1000 * (twoCoinsAboveMedianDownCoin + twoCoinsBelowMedianUpCoin) / data.length) / 10 |number:1 }}% {{aboveMedianDownCoin + belowMedianUpCoin | number}} {{twoCoinsAboveMedianDownCoin + twoCoinsBelowMedianUpCoin | number}} {{marketcoin ? periodLabel + ' UD+DU' : ' HT+TU'}} Expected: 25.0% {{(data.length / 4) | number:0}} {{marketcoin ? periodLabel + ' UU' : ' HH'}} Observed: {{Math.round(1000 * aboveMedianUpCoin / data.length) / 10 |number:1 }}% Observed: {{Math.round(1000 * twoCoinsAboveMedianUpCoin / data.length) / 10 |number:1 }}% {{aboveMedianUpCoin | number}} {{twoCoinsAboveMedianUpCoin | number}} {{marketcoin ? periodLabel + ' UU' : ' HH'}} Expected: 25.0% {{(data.length / 4) | number:0}} {{marketcoin ? periodLabel + ' DD' : ' TT'}} Observed: {{Math.round(1000 * belowMedianDownCoin / data.length) / 10|number:1 }}% Observed: {{Math.round(1000 * twoCoinsBelowMedianDownCoin / data.length) / 10|number:1 }}% {{belowMedianDownCoin | number}} {{twoCoinsBelowMedianDownCoin | number}} {{marketcoin ? periodLabel + ' DD' : ' TT'}} Expected: 25.0% {{(data.length / 4) | number:0}} {{marketcoin ? periodLabel + ' UD' : ' HT'}} Observed: {{Math.round(1000 * belowMedianUpCoin / data.length) / 10|number:1 }}% Observed: {{Math.round(1000 * twoCoinsBelowMedianUpCoin / data.length) / 10|number:1 }}% {{belowMedianUpCoin | number}} {{twoCoinsBelowMedianUpCoin | number}} {{marketcoin ? periodLabel + ' UD' : ' HT'}} Expected: 25.0% {{(data.length / 4) | number:0}} {{marketcoin ? periodLabel + ' DU' : ' TH'}} Observed: {{Math.round(1000 * aboveMedianDownCoin / data.length) / 10 |number:1}}% Observed: {{Math.round(1000 * twoCoinsAboveMedianDownCoin / data.length) / 10 |number:1}}% {{aboveMedianDownCoin | number}} {{twoCoinsAboveMedianDownCoin | number}} {{marketcoin ? periodLabel + ' DU' : ' TH'}} Average Results of 1,000 Trials of {{data.length | number}} Flips Coin/Coin Coin/Market % of each outcome Run Trial Again Flip Again Coin / Coin When flipping two standard coins, there are four possible outcomes: Heads on both coins (HH), Tails on both coins (TT), Heads on the first coin and Tails on the second (HT), or Tails on the first coin and Heads on the second (TH). Each of these outcomes is equally likely. Since there are four possible outcomes, the probability of each outcome is 25%. Coin / Market If the direction of the market, relative to the median return, resembles a coin flip and you have a MarketCoin with UP on one side and DOWN on the other, you now have a situation that is like flipping two coins. The MarketCoin is shown on the left and an Index Portfolio coin on the right. The table below shows the expected 25% probability of each outcome and observed outcomes for each flip of the coins. The observed daily flipping of the MarketCoin (U or D) compared to the actual daily returns of the index portfolio coin (U or D) illustrates that the index portfolio is a reasonable substitute for a second coin based on similarity of the observed outcomes of each test to the expected outcomes of 2 coins. U = Up - Above the Median Return D = Down – Below the Median Return H = Heads side of coin T = Tails side of coin Swap Coins ▼ Statistician Series {{coin.name}} Tune Out the Noise Series {{coin.name}} Additional Coins {{coin.name}} Daily Monthly