source: db-scripts/p6-relational-algebra/p6_q4_annual_investing_diversification_concentration_ra.txt

IB <- pi_{iu.user_id, u.username, u.email}
      (investor_users iu bowtie_{iu.user_id = u.user_id} users u)

AAL <- pi_{a.user_id, a.ticker_symbol,
           COALESCE(a.quantity,0)->quantity,
           COALESCE(a.buy_price,0)->buy_price,
           COALESCE(a.quantity,0)*COALESCE(a.buy_price,0)->invested_amount,
           a.buy_date}
       (sigma_{YEAR(a.buy_date)=Y}(assets a))

TR <- gamma_{user_id, ticker_symbol;
             SUM(quantity)->total_quantity,
             SUM(invested_amount)->total_invested_amount,
             COUNT(*)->lot_count,
             MIN(buy_date)->first_buy_date,
             MAX(buy_date)->last_buy_date}(AAL)

PT <- gamma_{user_id;
             SUM(total_invested_amount)->annual_total_invested,
             SUM(lot_count)->annual_lot_count,
             COUNT(*)->distinct_tickers}(TR)

W0 <- TR bowtie_{TR.user_id = PT.user_id} PT
W1 <- alpha_{total_invested_amount/NULLIF(annual_total_invested,0)->position_weight}(W0)
W  <- omega_{PARTITION BY user_id ORDER BY total_invested_amount DESC, ticker_symbol ASC;
             DENSE_RANK()->position_rank}(W1)

C <- gamma_{user_id;
            SUM(position_weight*position_weight)->hhi_concentration,
            MAX(position_weight)->top_position_weight,
            MAX_IF(ticker_symbol, position_rank=1)->top_ticker}(W)

IBM <- IB x M
AY  <- sigma_{YEAR(a.buy_date)=Y}(assets a)
MI0 <- IBM leftouterjoin_{IBM.user_id=a.user_id AND IBM.month_no=MONTH(a.buy_date)} AY
MI  <- gamma_{user_id, month_no;
              SUM(COALESCE(a.quantity,0)*COALESCE(a.buy_price,0))->monthly_invested_amount}(MI0)
MS  <- gamma_{user_id;
              AVG(monthly_invested_amount)->avg_monthly_contribution,
              STDDEV_SAMP(monthly_invested_amount)->contribution_stddev,
              COUNT_IF(monthly_invested_amount>0)->active_investing_months}(MI)

R0 <- IB
      leftouterjoin_{IB.user_id=PT.user_id} PT
      leftouterjoin_{IB.user_id=C.user_id} C
      leftouterjoin_{IB.user_id=MS.user_id} MS
R1 <- alpha_{COALESCE(annual_total_invested,0)->annual_total_invested_nz,
             COALESCE(annual_lot_count,0)->annual_lot_count_nz,
             COALESCE(distinct_tickers,0)->distinct_tickers_nz,
             COALESCE(avg_monthly_contribution,0)->avg_monthly_contribution_nz,
             COALESCE(active_investing_months,0)->active_investing_months_nz,
             COALESCE(active_investing_months,0)/12.0->activity_ratio,
             COALESCE(hhi_concentration,0)->hhi_concentration_nz,
             1-COALESCE(hhi_concentration,1)->diversification_index,
             COALESCE(top_position_weight,0)->top_position_weight_nz,
             COALESCE(contribution_stddev/NULLIF(avg_monthly_contribution,0),0)->contribution_volatility_cv}(R0)
R  <- omega_{ORDER BY diversification_index DESC,
                    annual_total_invested_nz DESC,
                    active_investing_months_nz DESC,
                    user_id ASC;
             DENSE_RANK()->investing_annual_rank}(R1)