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Calculate the Capital Gains Overhang for Stocks A & B using the price and volume information
provided below (workings out must be shown). Assume that the reference point is calculated using
a 50/50 mix of the purchase price and the maximum price. Using your calculations, advise if an
investor should purchase stock A or B?
Stock Price
24
22
22
20
20
20
18
18
Share Price (£)
18
17
17
16
15
15
14
14
12
12
12
10
1
2
3
4.
5
6
Month
Stock A
Stock B
Stock Volume
25%
20%
15%
10%
5%
II
II
0%
1
2
3
4
5
6
Month
Stock A Stock B
1. Calculate the Capital Gains Overhang (CGO) for Stock A and B and
provide a buy/sell recommendation based on your answer for each
stock.
Stock A
Stock B
Price
10
Month
1
2
3
4
5
6
12
15
13
17
14
Turnover
10%
10%
10%
10%
10%
15%
Month
1
2
3
4
5
6
Price
20
22
23
22
20
25
Turnover
10%
10%
20%
20%
10%
10%
1. Calculate the Capital Gains Overhang (CGO) for Stock A and B and
provide a buy/sell recommendation based on your answer for each
stock.
Stock A
Price
10
Month
1
2
3
4
5
6
12
Turnover
10%
10%
10%
10%
10%
15%
Ref
1.12
1.49
2.07
15
Adjusted
Turnover
5.58%
6.20%
6.89%
7.65%
8.50%
15.00%
49.81%
Weighted Turnover
11.20%
12.44%
13.82%
15.36%
17.07%
30.12%
100.00%
13
17
14
2.00
2.90
4.22
13.80
CGO
18.82%
Stock B
Month
Price
Ref
Turnover
10%
20
10%
u w NP
22
23
3
Adjusted
Turnover
4.67%
5.18%
12.96%
16.20%
9.00%
10.00%
58.01%
Weighted
Turnover
8.04%
8.94%
22.34%
27.93%
15.51%
17.24%
100.00%
20%
20%
10%
10%
4
22
1.61
1.97
5.14
6.14
3.10
4.31
22.27
20
6
25
CGO
-11.35%
Recommendation: Stock A has a positive CGO. Therefore, it is likely to be
undervalued, so the investor should BUY. Stock B has a negative CGO.
Therefore, it is likely to be overvalued, so the investor should SELL.
The CGO Variable
Pt-1-RE
CGO4 =
Pt-1
Where: p=share price, r=reference point
Share price is lagged by 1 period
• Positive CGO when the current share price is
above the reference point.
Negative CGO when the current share price is
below the reference point.
Risk Preferences
VALUE
• Positive CGO means
that an investor is in the
gains portion of the
curve leading to risk
aversion.
LOSSES
A
GAINS
O
Negative CGO means
that an investor is in the
loss portion of the
curve- leading to risk
seeking.
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Capital Gains Overhang (CGO)
3
Implication for Share Prices
Development
• Developed in 2005 in a paper
Grinblant and Han
• Uses Prospect Theory is evaluate if a stock is currently
undervalued or overvalued.
. Elements of Prospect Theory utilised:
1. The reference point explicitly
2. The value function implicity
3. The decision weighting function is not used
Positive CGO
Shares Underpriced
4
19
Outperform
The CGO Variable
Peas – Re
CGO, P-
where the prin
Share prices and per
• Positive CGO when the current share price is
above the reference point.
• Negative CGO when the current share price is
below the reference point.
5
Risk Preferences
Negative CGO
Shares Overpriced
• Positive CGO means
that an investor is in the
gains portion of the
curve – loading to risk
aversion

11
• Negative CGO means
that an investor is in the
loss portion of the
curve- leading to risk
seeking
Underperform
6
Implication for Share Prices
Risk Preferences
Positive CGO –
Shares Underpriced
Outperform
• Positive CGO means
that an investor is in the
gains portion of the
curve – leading to risk
aversion
Negative CGO –
LOSSES
Shares Overpriced
Underperform
X
• Negative CGO means
that an investor is in the
loss portion of the
curve- leading to risk
seeking
7
Screen Shot 202….png
Screen Shot 202….png
Screen Shot 202….png
Show all
Ñ…
Implication for Share Prices
Positive CGO
Shares Underpriced
Outperform
11 11
Negative CGO
Shares Overpriced
Underperform
The Aggregate Reference Point
• The CGO Model uses the investor’s purchase
price as the reference point.
• But we have a problem. How can we measure
the aggregate reference point for all for investors
in a stock?
– Investors will buy and sell on different days.
– Investors will buy and sell at different prices.
The CGO Variable
Pt-1-RE
CGO4 =
Pt-1
Where: p=share price, r=reference point
Share price is lagged by 1 period
• Positive CGO when the current share price is
above the reference point.
Negative CGO when the current share price is
below the reference point.
Risk Preferences
VALUE
• Positive CGO means
that an investor is in the
gains portion of the
curve leading to risk
aversion.
LOSSES
A
GAINS
O
Negative CGO means
that an investor is in the
loss portion of the
curve- leading to risk
seeking.
Implication for Share Prices
Positive CGO
Shares Underpriced
Outperform
11 11
Negative CGO
Shares Overpriced
Underperform
Implication for Share Prices
Positive CGO
Shares Underpriced
Outperform
11 11
Negative CGO
Shares Overpriced
Underperform
The Aggregate Reference Point
• The CGO Model uses the investor’s purchase
price as the reference point.
• But we have a problem. How can we measure
the aggregate reference point for all for investors
in a stock?
– Investors will buy and sell on different days.
– Investors will buy and sell at different prices.
Turnover Adjusted Reference Point
• The CGO Model uses the turnover adjusted price
to overcome the problem.
Turnover(V)
=
Shares Traded
Shares Outstanding
So months on which there are a higher turnover, will
receive a greater weight in the aggregate reference point.
An Example
• So lets assume, the turnover is 10% per month
over the last 6 months.
The aggregate reference point would be?
Month
Turnover
Price
1
10%
10
10%
12
10%
15
ar A WN
10%
9
10%
11
CO
10%
13
An Example- Adjusted Turnover
• But we need to account for the fact that some
investors who buy in the earlier months will
subsequently sell before the end of month 6.
• For example, in month 5, 10% of investors who
purchase then will sell out in month 6.
• True turnover in month 5 is: 10%*(1-10%)=9%
An Example- Adjusted Turnover
• In month 4, 10% if investors who purchase then
will sell out in month 5 and then another 10% will
sell out in month 6.
True turnover in month 4: 10%*(1-10%)2 =8.1%
• Month 3: 10%*(1-10%)3 = 7.29%
• Month 2: 10%*(1-10%)4 =6.56%
• Month 1: 10%*(1-10%)5 =5.91%
Adjusted Turnover
O
So we can add the adjusted turnover to the table.
Month
Price
Ref Point
Turnover Adj
Turnover
1
10%
5.91%
10
2
10%
6.56%
12
3
10%
7.29%
15
4
10%
8.1%
9
5
10%
9%
11
6
10%
10%
13
46.86%
But we still have a problem as the adjusted turnover does
not sum to 100%.
Weighted Adjusted Turnover
So we can add the adjusted turnover to the table.
Month
Turnover
Adj
Turnover
Weighted Adj
Turnover
12.61%
1
10%
5.91%
2
10%
6.56%
14%
3
10%
7.29%
15.55%
4
10%
8.1%
17.29%
5
10%
9%
19.21%
6
10%
10%
21.34%
46.86%
100%
Calculating the Reference Point
O
• Now we are ready to calculate the reference point.
Month
Turnover
Adj
Turnover
Weighted Adj Price
Turnover
Ref
Point
1
10%
5.91%
12.61%
10
1.261
2
10%
6.56%
14%
12
1.68
3
10%
7.29%
15.55%
15
2.33
4
10%
8.1%
17.29%
9
1.56
5
10%
9%
19.21%
11
2.11
6
10%
10%
21.34%
13
2.77
46.86%
100%
11.71
Calculating CGO
• So we have the aggregate reference point. What
is the CGO of the stock?
Pt-1 – Rt
CGO
=
Pt-1
CG0t
11 – 11.71
= -6.46%
11
Concluding our Example
• So the stock has a negative CGO.
• The CGO model suggests this stock is
overvalued and will underperform in the future.
O
• We can calculate the CGO for any stock in the
market using only price and volume (turnover)
information to assess if it under or over-valued.

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