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Yale School of Management
Emerging Market Finance
Lecture 11: Valuation of Illiquid Securities
Challenge: shares and other securities are
often illiquid in emerging markets! How
much should you value them?
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Yale School of Management
Evidence on Illiquidity DiscountsSilber (1991): Rule 144 letter stocks: average
discount of 34% (based on 69 private transactions, from 1981-88)
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Discount Size and Firm Characteristics: the U.S. Sample
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Discounts on Illiquid Bonds
Amihud and Mendelson (1991) and Kamara (1994): yield spread between illiquid notes and liquid Treasury bills = 35 basis points.
Boudoukh and Whitelaw (1991), the yield spread = 50 basis points between designated benchmark bond and less liquid government bonds in Japan.
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Yale School of Management
China’s Experience with Illiquid Stocks
State Shares: owned by the state and not publicly tradable
Restricted Institutional Shares (RIS): held only by institutions (financial and otherwise), and never publicly tradable
Floating common shares: A-shares and B-
shares
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The RulesState shares can only be transferred to other
institutions privately
RIS shares are officially only transferable via private search and negotiations. But, since Dec. 1998, auction houses have been selling RIS shares in semi-public auctions
Regardless of share type, no short-selling is allowed.
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Typical Ownership Pie
State37%
RIS28%
A-shares30%
B-shares5%
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To first examine price discounts, we use two sets of data: the auction data
2,577 RIS auction transactions from August 2000 to June 2001, on 18 auction houses mostly in Shanghai. Total stocks auctioned: 258
Auctions take place on weekends and eveningsParticipants have to be “institutions” (mostly,
private-fund management firms)Auction houses advertise in advance
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Yale School of Management
Private-Placement Sample
242 transactions
Aug. 2000 to July 2001
Much larger blocks
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Summary Statistics for AuctionsRIS Auction Transactions
Price Discount
Trans. Value ( in 1,000
yuan)
Trans. Size ( in 1,000
shares)
Auction B/P
Auction E/P
Avg. 77.93% 622 204 0.76 0.04
(Std. Dev.)
(6.65%) (674) (242) (0.42) (0.08)
Med 78.90% 424 136 0.67 0.05
Max 97.22% 28,800 12,000 3.60 0.34
Min 36.98% 13 5 0.00 -0.39
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Yale School of Management
What Does the Discount Mean?
Suppose you have two firms with identical future cashflow and operating under identical environments
But, firm A is publicly traded, while firm B is privately owned.
Then, firm B’s worth is only 21% of firm A’s, simply because firm B is private!
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Yale School of Management
Summary Statistics for Private Placements
Price Discount
Trans. Value ( in 1,000
yuan)
Trans. Size ( in 1,000 shares)
B/P E/P
Avg. 85.59% 76,340 31,800 1.16 0.04
(Std. Dev.)
(8.32%) (72,940) (26,870) (1.74) (0.02)
Med 87.03% 52,570 24,570 0.97 0.05
Max 99.40% 494,810 326,830 20.39 0.46
Min 56.28% 270 510 0.00 -0.62
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Discounts across B/M Groups
80.74%
91.74%
78.58%
89.63%
77.56%
86.57%
75.43%
83.92%
72.57%
78.74%
70%
75%
80%
85%
90%
95%
Avg
Dis
coun
t
Low MediumB/M Ratio
High
RIS Discounts by B/M Ratio
Blue: auctions
Red: private-trans.
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Yale School of Management
Discounts by Auction Quantity
74.47%
89.03%
74.99%
88.19%
77.00%
83.49%
78.06%
85.79%
80.14%82.62%
70%
75%
80%
85%
90%
Avg
Dis
cou
nt
Low MidAuction-Quant
High
Average Discounts Across Transaction Quantity Groups
Blue: auctions
Red: private-trans.
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Yale School of Management
Discounts by Fraction of RIS Shares in Ownership Structure
75.04%
84.43%
74.58%
85.68%
77.99%81.92%
79.06%
87.83%
78.18%
87.84%
70%
75%
80%
85%
90%
Avg
Dis
cou
nt
SmallShare
Mid-Level LargeShare
RIS as Fraction of All Shares Outstanding vs Discounts
Blue: auctions
Red: private-trans.
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Yale School of Management
Discounts by Age (since IPO)
79.72
75.86
73.09
86.2685.42
88.25
70
72
7476
78
80
82
8486
88
90
< 2 Years Between 2 & 7 Yrs 7 Yrs & Older
Avg
Dis
cou
nt
(%)
Blue: auctions & Red: private transfers
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Yale School of Management
Future Investment Returns in RISAssume the trading restriction is lifted in T years
(uncertainty). Share price at time of lifting is unknown. Adopt “buy & hold”
Annual returns from holding RIS until the restriction is lifted inShare Price at Time of Lifting T=1 Yr T=2 Yrs T=3 Yrs T=5 Yrs T=10 Yrs
50% of Today's Price 127.27% 50.76% 31.48% 22.78% 17.84%
75% of Today's Price 240.91% 84.64% 50.50% 35.88% 27.80%
100% of Today's Price 354.55% 113.20% 65.65% 46.01% 35.37%
125% of Today's Price 468.18% 138.37% 78.44% 54.39% 41.55%
150% of Today's Price 581.82% 161.12% 89.62% 61.59% 46.80%
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Are the RIS Auction Prices Reasonable?
The answer lies in the rules.
Three rules are binding, each causing a distortion:
RIS shares not tradable, but transferable No short-selling allowed (binding for floating shares) RIS shares only for institutions, not for the public.
Let’s look at two types of models.
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Longstaff’s (1995) Model
Assumption: the illiquid stock is locked up for some T years (not tradable at all).
Then, the upper bound on the price discount:
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Yale School of Management
Longstaff’s (1995) Model
1)exp()()2(/1)( 8222
2222 TTTT NPpTD
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Yale School of Management
Upper Bounds on Illiquidity Discounts: Longstaff (1995) Model
20%
30%
40%
50%
60%
70%
80%
90%
100%
110%
1 2 3 4 5 6 7 8 9 10
Years before the trading restriction is lifted
Illi
qu
idit
y D
isco
un
t U
pp
erB
ou
nd
Sigma=30%
Sigma=40%
Sigma=43.5%
Sigma=50%
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Yale School of Management
Amihud and Mendelson (1986) Model
Liquid stock: no trading costsRIS transferable “privately”, but not tradable publicly,
means it is MORE costly to exchange ownership Let c be the % search/transaction cost for RIS (whenever there is a
buy or sell). Put aside the no-short-selling aspect for now.
Then, relative to the fair value of a floating share, the discount for RIS is
d = PV(all future transaction costs)
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Table for Fair Non-Marketability Discount (without short-selling constraint)
Assume c = 5%. T = # of yrs before lifting, t = # of yrs in a typical RIS holding period.Cost of capital = 10% per year
T = 1 year T = 2 years T = 3 years T = 5 years T = 10 yearsAvg holding periodt = 1/2 year -14.52% -32.23% -48.29% -76.08% -100.00%
t = 1 year -5.00% -14.09% -22.36% -36.70% -62.59%
t = 2 years -5.00% -5.00% -13.26% -20.09% -30.40%
Years before lifting restriction
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Discount due to No-Short-Selling
With No-Short-Selling, stock prices can be far above fundamentals, yet no one can do anything about it.
Due to its emerging-market status, suppose the right P/E for China is 30.
Relative to the floating-share price, a reasonable discount should be
No-Short-Selling discount + Non-Marketability discount
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Yale School of Management
Illiquidity Discounts based on Amihud & Mendelson (1985)
70%
75%
80%
85%
90%
95%
Years before RIS Trading Restriction is Lifted
Illiq
uid
ity D
isco
un
t
Avg. holding period = 1 yr.
Avg. holding period = 1.5 yrs.
Avg. holding period = 2 yrs.
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Yale School of Management
Restricted vs Floating Shares:
a cause for other things Everyone wants to go IPO! No one wants to
stay private, even if it means they have to take risk and make up the numbers!
With relatively few shares floating, easy to manipulate common share prices!
leading to “pyramid corporate family empire”.
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With such discounts, every public corp. will be run like a “hedge fund”
With the RIS shares priced so low, takes only little capital to acquire a “controlling shareholder” position
The price discount for RIS shares relative to floating A-shares is so high (84% avg.) that every firm wants to be a “hedge fund”:
Long RIS (or, state shares) and get the right to short floating A-shares.
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“Hedge Fund” Strategy
Public Company ABC
Pay $0.16 to acquire an RIS or state share, to become “controlling shareholder”
Sell floating A-shares to public at $1 per share.
Transfer cash through “related-party” transactions
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Yale School of Management
Sample for the Control Premium
154 private transfers of state-owned shares (SOS) to other state-owned enterprises (SOE) (with 91 transfers involving controlling blocks and the other 63 transfers non-controlling blocks)
17 transfers of controlling SOS share blocks to private firms, and 3 non-controlling SOS share blocks to private firms.
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Yale School of Management
Control Premium Size
4.45%
7.93%
0.82%
21.63%
0%
5%
10%
15%
20%
25%
国营非控股 国营控股 民营非控股 民营控股
% SOS price premium relative to book value of equity per share
Control Blocks to private firms
Non-Control Blocks to
private firms
Control Blocks to SOEs
Non-Control Blocks to SOEs
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Yale School of Management
Control Premium Relative to Floating A-Share Prices
18.05%
16.09%
20.10%18.65%
0%
5%
10%
15%
20%
25%
国营非控股 国营控股 民营非控股 民营控股Control Blocks to private firms
Non-Control Blocks to
private firms
Control Blocks to SOEs
Non-Control Blocks to SOEs
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Yale School of Management
Control Premium Relative to Revenue Per Share
1.2
1.5
3.75
1.66
0
1
1
2
2
3
3
4
4
国营非控股 国营控股 民营非控股 民营控股Control Blocks to private firms
Non-Control Blocks to
private firms
Control Blocks to SOEs
Non-Control Blocks to SOEs
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ROE Across Groups
8.75%
6.83%
0.56%
8.67%
0%
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
国营非控股 国营控股 民营非控股 民营控股Control Blocks to private firms
Non-Control Blocks to
private firms
Control Blocks to SOEs
Non-Control Blocks to SOEs
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Yale School of Management
ROA across Groups
3.53%3.37%
0.44%
3.17%
0%
1%
1%
2%
2%
3%
3%
4%
4%
国营非控股 国营控股 民营非控股 民营控股Control Blocks to private firms
Non-Control Blocks to
private firms
Control Blocks to SOEs
Non-Control Blocks to SOEs