In Portfolio$123,$ create a ranking system based on the following combination of signals:

i$)40\%$ Quality

i$\mathrm{.}1)50\%$ Gross Profitability: GrossProfitTTM$/$AstTotQ

i$\mathrm{.}2)50\%$ Piotroski Score: PiotFScore

ii$)20\%$ Trends

ii$\mathrm{.}1)100\%$ Momentum: $(1+$ Ret$1$Y$\%$Chg $/100)/(1+$ Ret$4$W$\%$Chg $/100)$

iii$)40\%$ Information

iii$\mathrm{.}1)50\%$ Trading Volume Acceleration: Vol$10$DAvg$/$Vol$3$MAvg

iii$\mathrm{.}2)50\%$ Analyst Disagreement: NextFYEPSStdDev$/$Abs$($NextFYEPSMean$)$

Analyst Disagreement is a negative signal $($i$.$e$.,$ lower is better$).$

Backtest over two time periods as instructed below:

Time period: MAX or LAST $10$ years.

Universe: PRussell$3000$

Benchmark: Russell $3000$

Rebalancing Frequency: every $4$ weeks

Number of buckets$=10$

ALL THE OTHER OPTIONS: use P$123$ default settings.

Which of the options below comes closest to the SPREADS of the two backtests?

MAX: $19\%$ per year; LAST $10$ YEARS: $14\%$ per year.

MAX: $15\%$ per year; LAST $10$ YEARS: $4\%$ per year.

MAX: $20\%$ per year; LAST $10$ YEARS: $4\%$ per year.

MAX: $17\%$ per year; LAST $10$ YEARS: $5\%$ per year.

MAX: $16\%$ per year; LAST $10$ YEARS: $16\%$ per year.

MAX: $15\%$ per year; LAST $10$ YEARS: $13\%$ per year.

MAX: $22\%$ per year; LAST $10$ YEARS: $16\%$ per year.

MAX: $17\%$ per year; LAST $10$ YEARS: $9\%$ per year.

MAX: $14\%$ per year; LAST $10$ YEARS: $17\%$ per year.

MAX: $12\%$ per year; LAST $10$ YEARS: $10\%$ per year.

Consider the backtests over the MAX time period and over LAST $10$ years period from Question $1.$ Did the predictive factors "work" in predicting returns over the MAX time period? And over the LAST $10$ years? Explain.

Consider the backtests from Question $1.$ Describe the background calculations Portfolio$123$ uses to generate the Total Return bar graphs. Be as precise as you can so that a person that knows nothing about Portfolio$123$ or backtesting can reproduce the results if given all the data.

Consider the backtest over the MAX time period in Question $1.$ Consider an investor that, in January $1999,$ invested $$10,000$ in the dynamic investment strategy corresponding to Bucket $10$ of the backtest. Assume the investor followed the strategy from then until today without withdrawing any cash. According to backtest results, and ignoring any taxes, approximately how much money the investor would have today? Again ignoring taxes, can you name one reason why the investor would in fact have less money than that today because the Question $1$ backtest ignores an important real world consideration?

Can backtests such as the one on Question $1$ potentially inform the debate on whether stock markets are efficient? Why? Why not? Explain.

Consider the ranking system in Question $1.$ Use the Grinold$-$Kahn procedure to estimate the difference between the return of Zoetis $($ticker ZTS$)$ and the return of Russell $3000$ Index over the next $12$ months. That estimate is closest to:

$0\%.$

$-1\%.$

$-2\%.$

$+1\%.$

$+3\%.$

$+2\%.$

$-3\%.$