The Friendship Theorem

Publication loaded info list link PDF Page 1 / 3 fullscreen remove_circle_outline add_circle_outline search group_add more_horiz get_app T ABLE 2. Estimates of TEAM insolvency risk over multiyear horizon. μ = σ = . 15, c = . 05, C 0 = S 0 = 0 . 5 Investment Horizon ( n ) 5 10 15 20 25 S ′ 0 .7318 1.178 1.898 3.058 4.929 E ( T ′ n ) 1.721 3.457 7.716 18.11 43.13 E ( B n ) 1.644 2.837 5.108 9.510 18.15 √ Va r ( T ′ n ) = √ Va r ( B n ) .2984 .8671 2.183 5.184 11.92 α 1.366 .8486 .5269 .3270 .2029 Insolvency Risk: Lower Bound 4 . 01 × 10 − 9 3 . 45 × 10 − 5 .00085 .0066 .0258 Monte Carlo 0 6 . 67 × 10 − 5 .00333 .0220 .0696 Upper Bound 4 . 50 × 10 − 9 1 . 85 × 10 − 4 .00738 .0523 .1692 uous, although we can imagine a high-stakes player attempting to implement such a strategy. REFERENCES 1. F. Gerth III, The TEAM approach to investing, Amer. Math. Monthly 106 (1999) 553–558. 2. W. Y. Lee, Diversification and time: Do investment horizons matter?, J. Portfolio Mgt. 16 (Spring 1990) 21

Publication loaded info list link PDF Page 1 / 3 fullscreen remove_circle_outline add_circle_outline search group_add more_horiz get_app T ABLE 2. Estimates of TEAM insolvency risk over multiyear horizon. μ = σ = . 15, c = . 05, C 0 = S 0 = 0 . 5 Investment Horizon ( n ) 5 10 15 20 25 S ′ 0 .7318 1.178 1.898 3.058 4.929 E ( T ′ n ) 1.721 3.457 7.716 18.11 43.13 E ( B n ) 1.644 2.837 5.108 9.510 18.15 √ Va r ( T ′ n ) = √ Va r ( B n ) .2984 .8671 2.183 5.184 11.92 α 1.366 .8486 .5269 .3270 .2029 Insolvency Risk: Lower Bound 4 . 01 × 10 − 9 3 . 45 × 10 − 5 .00085 .0066 .0258 Monte Carlo 0 6 . 67