Mike, relax, get comfortable. Here goes:
The reason the average gain CAN be negative but the 52 wk extrapolated CAN be positive is that the winners can easily exceed 100 % gain but even the biggest loser can not exceed 100 % loss.(We are ignoring commissions.) In other words, for the current period, you take the average of the current change. But for the 52 wk average change, you must FIRST project each current change to a 52 wk price for all 43 stocks, compute that % change for each stock, and THEN take the average of the 43 stock yields.. You can't take the current average change for the combined 43 stocks and then extrapolate that change over 52 wks.
In all of the examples, we have to assume the current performance continues at the same rate. ( This will of course create unrealistic highs and similarly unrealistic lows, but as the year goes on, it will become more accurate.)
Example
STOCK A UP 30 % ($1000 of A is now worth $1300)
STOCK B DOWN 50 %($1000 of B is now worth $500)
Average is (50-30)/2 = DOWN 10 % thru 6 weeks ($2000 of A&B is now worth $1800)
Six weeks are completed and there are 8.666667 of these 6 wk periods in a 52 wk time period. 8.666667 is the number of compounding periods(the exponent in the compound yield calculation).
If you improperly took the 10 % decline and extrapolated this over 52 weeks, you would get the following:Start Price*((.90 ^ 8.666667)= .4013 or DOWN 59.87 % or $1197.40 loss.
But wait, if I start with $2000 in two stocks, with one on a roll and the other tanking, how can I be down nearly $1200 at the end of the year. I can't lose more than $1000 on the loser and the winner is surely on pace to be worth more than $1000. Right?
The correct procedure:
Projected to 1 yr, or 8.6667 time periods of 6 weeks each,
Stock A price is Start Price*((1.30) ^ 8.666667)=Start Price*8.9028 or
UP 790.28 % ($1000 of A will be worth $8902.80 after 52 weeks
Stock B price is Start Price*((.5) ^ 8.666667)=Start Price*.00246 or DOWN 99.75 % ($1000 of B will be worth $2.50 after 52 weeks
Together, they will be worth $8905.30 or $6905.30 growth on $2000 or UP 345.265%
or you can compute the average change by taking: (790.28-99.75)/2=+345.265 %
Same answer.
Q.E.D.
TG |
