# Balance vector

N.B: this concept may be adequately captured by the zero crossing frequency (see [circularity of trade](/CMlnVwUjR6-EPA4jHyqsqw)).

A [balance](/R1iAIsZoRRmJgIV4NlHQZw) figure with a gradient across the [analysis period](/conspoQ5TNmH5pfZqp-LfQ). This could of course be 'horizontal' - a fixed balance, like zero (or a positive or negative number), or it could be a trend line of some kind - either desirable or derived.

{
    "$schema": "https://vega.github.io/schema/vega-lite/v4.json",
    "data": {
        "values": [
            {"period": 1, "balance": 10, "member": "1"},
            {"period": 2, "balance": 100, "member": "1"},
            {"period": 3, "balance": -75, "member": "1"},
            {"period": 4, "balance": -0, "member": "1"},
            {"period": 5, "balance": 80, "member": "1"},
            {"period": 6, "balance": -120, "member": "1"},
            {"period": 7, "balance": 50, "member": "1"},
            {"period": 8, "balance": 170, "member": "1"},
            {"period": 9, "balance": -30, "member": "1"},
            {"period": 10, "balance": -80, "member": "1"},
            {"period": 11, "balance": 100, "member": "1"},
            {"period": 12, "balance": 10, "member": "1"},
            {"period": 1, "balance": -10, "member": "2"},
            {"period": 2, "balance": 10 , "member": "2"},
            {"period": 3, "balance": 14, "member": "2"},
            {"period": 4, "balance": 20, "member": "2"},
            {"period": 5, "balance": 30, "member": "2"},
            {"period": 6, "balance": 40, "member": "2"},
            {"period": 7, "balance": -10, "member": "2"},
            {"period": 8, "balance": 20, "member": "2"},
            {"period": 9, "balance": -10, "member": "2"},
            {"period": 10, "balance": 30, "member": "2"},
            {"period": 11, "balance": -20, "member": "2"},
            {"period": 12, "balance": -10, "member": "2"},
            {"period": 1, "balance": -50, "member": "3"},
            {"period": 2, "balance": -100 , "member": "3"},
            {"period": 3, "balance": -20, "member": "3"},
            {"period": 4, "balance": -120, "member": "3"},
            {"period": 5, "balance": -30, "member": "3"},
            {"period": 6, "balance": -80, "member": "3"},
            {"period": 7, "balance": -120, "member": "3"},
            {"period": 8, "balance": -10, "member": "3"},
            {"period": 9, "balance": -90, "member": "3"},
            {"period": 10, "balance": -50, "member": "3"},
            {"period": 11, "balance": -100, "member": "3"},
            {"period": 12, "balance": -40, "member": "3"}
        ]
    },
    "mark": "bar",
    "encoding": {
        "column": {
            "field": "period", "type": "nominal", "sort": "false", "spacing": 0 , "title": "Measurement Intervals" 
        },
        "x": {
            "field": "member", "type": "ordinal",
            "axis": {
                "domain": false,
                "ticks": false,
                "labelAngle": 0
                
            }
        },
        "y": {
            "field": "balance", "type": "quantitative",
            "axis": {
                "gridColor": {
                    "condition": {"test": "datum.value === 0", "value": "black"}, "value": "#ddd"                    
                }
            }
        },
    "color": {
      "field": "member",
      "scale": {"range": ["#6756ad", "#ca8123", "#23511a"]}
    }
    } 
}

In these examples, member balances are recorded at the end of each measurement interval. The analysis period is comprised of all the measurement intervals. Considering balances in the first and last intervals :

- $M_1$'s balance returns to its initial value with a high turnover in the interim;
- $M_2$'s balance also shows zero net change but with a smaller turnover;
- $M_3$'s balance has increased, with a turnover somewhere between the other two.

The tendency of a member's account balance to return to some average value/[balance vector](/RK0pk9ncTfOugxtb22ZiyA) is termed its '[elasticity](/rKATqIzhTpic1F9pkpDmew).'

A further issue is the choice of [analysis period](/conspoQ5TNmH5pfZqp-LfQ). The following example has three entities with broady circular trade over a 12 interval period - but exhibiting different seasonal pattersn (1 might be a framer with a cash crop, 2 might be a retailer with a big Christmas emphais, and 3 a summer holiday seasonal business). Each of these will look differnt depending upon the choice of analysis period, and no standard analysis period will give a comparable indicator for all.

{
    "$schema": "https://vega.github.io/schema/vega-lite/v4.json",
    "data": {
        "values": [
            {"period": 1, "balance": 50, "member": "1"},
            {"period": 2, "balance": 30, "member": "1"},
            {"period": 3, "balance": -10, "member": "1"},
            {"period": 4, "balance": -50, "member": "1"},
            {"period": 5, "balance": -80, "member": "1"},
            {"period": 6, "balance": -120, "member": "1"},
            {"period": 7, "balance": -150, "member": "1"},
            {"period": 8, "balance": 250, "member": "1"},
            {"period": 9, "balance": 200, "member": "1"},
            {"period": 10, "balance": 150, "member": "1"},
            {"period": 11, "balance": 100, "member": "1"},
            {"period": 12, "balance": 70, "member": "1"},
            {"period": 1, "balance": 250, "member": "2"},
            {"period": 2, "balance": 200 , "member": "2"},
            {"period": 3, "balance": 160, "member": "2"},
            {"period": 4, "balance": 100, "member": "2"},
            {"period": 5, "balance": 30, "member": "2"},
            {"period": 6, "balance": 60, "member": "2"},
            {"period": 7, "balance": -10, "member": "2"},
            {"period": 8, "balance": -20, "member": "2"},
            {"period": 9, "balance": -60, "member": "2"},
            {"period": 10, "balance": -50, "member": "2"},
            {"period": 11, "balance": 30, "member": "2"},
            {"period": 12, "balance": 120, "member": "2"},
            {"period": 1, "balance": -130, "member": "3"},
            {"period": 2, "balance": -60 , "member": "3"},
            {"period": 3, "balance": 10, "member": "3"},
            {"period": 4, "balance": 30, "member": "3"},
            {"period": 5, "balance": 40, "member": "3"},
            {"period": 6, "balance": 90, "member": "3"},
            {"period": 7, "balance": 200, "member": "3"},
            {"period": 8, "balance": 220, "member": "3"},
            {"period": 9, "balance": 200, "member": "3"},
            {"period": 10, "balance": 20, "member": "3"},
            {"period": 11, "balance": -20, "member": "3"},
            {"period": 12, "balance": -40, "member": "3"}
        ]
    },
    "mark": "bar",
    "encoding": {
        "column": {
            "field": "period", "type": "nominal", "sort": "false", "spacing": 0 , "title": "Measurement intervals" 
        },
        "x": {
            "field": "member", "type": "ordinal",
            "axis": {
                "domain": false,
                "ticks": false,
                "labelAngle": 0
                
            }
        },
        "y": {
            "field": "balance", "type": "quantitative",
            "axis": {
                "gridColor": {
                    "condition": {"test": "datum.value === 0", "value": "black"}, "value": "#ddd"                    
                }
            }
        },
    "color": {
      "field": "member",
      "scale": {"range": ["#6756ad", "#ca8123", "#23511a"]}
    }
    } 
}