Historical Results and Commentary
August 11, 2004
Holdings
|
|
Aug-04 |
|
1 |
F |
|
2 |
NBG |
|
3 |
YHOO |
|
4 |
NKE |
|
5 |
BA |
|
6 |
VRSN |
|
7 |
JDSU |
|
8 |
CAT |
|
9 |
JNJ |
|
10 |
NSM |
|
11 |
CA |
|
12 |
FNF |
|
13 |
MWD |
|
14 |
TKC |
|
15 |
HMC |
|
16 |
CRYP |
|
17 |
X |
|
18 |
AAPL |
|
19 |
COP |
|
20 |
ACH |
Performance of Individual Stocks For last 3 months:
|
Aug-04 |
|
|
FNF |
8.19% |
|
COP |
1.23% |
|
CAT |
-0.92% |
|
NKE |
4.41% |
|
BA |
16.07% |
|
VRSN |
-5.74% |
|
JDSU |
-2.22% |
|
YHOO |
2.47% |
|
JNJ |
2.09% |
|
NSM |
-36.96% |
|
CA |
-11.80% |
|
F |
-0.38% |
|
MWD |
-8.29% |
|
TKC |
32.45% |
|
HMC |
18.55% |
|
CRYP |
-26.88% |
|
X |
35.94% |
|
AAPL |
14.30% |
|
NBG |
-3.26% |
|
WB |
-0.50% |
Total Increase (Decrease) since last quarter: 1.94%
Additions: ACH
Subtractions: WB
Commentary: My commentary this quarter is on
the marginal investor, and his or her power in the market. At any given time, it is the people who are
trading who impact asset prices, not passive shareholders. In this way the market is analogous to
voting. Though only a small percentage
of people vote in the
On this minute level, do things work efficiently? Theory seems to say yes. But the following example I am about to present seems to imply that the actual price of a stock will be slightly higher than its intrinsic value.
Let’s take a hypothetical example. Suppose the ‘intrinsic value’ of AAPL is $29.5 per share, and there are 1,000 shares of AAPL in the universe. Let’s also assume that there are a large number (1,000) of investors in this model, and that such investors subscribe to a range of valuation estimates that are normally distributed around $29.50 with a standard deviation of around $1.00. Furthermore, each estimate receives equal weight in the market[1]. In other words, there are 1,000 analysts covering this stock and they each have an equal number of ears and dollars that listen to them. Where will the stock trade? It will trade at about $29.675, not at $29.50
Here is why: In most real life stock market decisions, the propensity to buy is proportional to the difference between the market price and the estimate of intrinsic value, whereas the propensity to sell is merely dependent upon the asset price being mores than the estimate of intrinsic value. I suppose that there are several ways to model the demand function. I have chosen a simple model whereby the demand for a stock is proportional to the percent at which a buyer feels it is overvalued:
Stock demand = [(estimated intrinsic value/market value)-1]*100[2]
Suppose the stock is at 29.5. Then, if we assume rational shareholders, all current shareholders will subscribe to the 50% of the most optimistic analysts in the coverage world. In other words, in figure 1, only analysts in yellow are listened to by people who actually own AAPL. They probably bought their shares from people listening to the purple analysts.[3]
However, within the population of shareholders, things are not at equilibrium at 29.5. This is because people who believe the stock is very close to its intrinsic value are not likely to hold copious quantities of it, while those who believe the stock is significantly undervalued will hold more of it. The following shows the intrinsic value estimates for people that actually would consider holding AAPL at 29.5:
But, the equilibrium state would not be having each of these 500 people holding 2 shares each. People with higher expectations of the value of the stock will hold more than those who feel the stock is priced about correctly. The following three tables estimate how demand-weighting brings the equilibrium price to 29.675:
|
Price=29.5 |
|
|
|
|
Intrinsic
Value Estimate |
Number of
Subscribers |
Shares/Person
demanded at given price |
Weighted
Demand |
|
29.5 |
39.8 |
0 |
0 |
|
29.6 |
39.5 |
0.338983051 |
13.38983051 |
|
29.7 |
38.6 |
0.677966102 |
26.16949153 |
|
29.8 |
37.5 |
1.016949153 |
38.13559322 |
|
29.9 |
36.1 |
1.355932203 |
48.94915254 |
|
30 |
34.2 |
1.694915254 |
57.96610169 |
|
30.1 |
32.3 |
2.033898305 |
65.69491525 |
|
30.2 |
30.1 |
2.372881356 |
71.42372881 |
|
30.3 |
27.8 |
2.711864407 |
75.38983051 |
|
30.4 |
25.4 |
3.050847458 |
77.49152542 |
|
30.5 |
23 |
3.389830508 |
77.96610169 |
|
30.6 |
20.6 |
3.728813559 |
76.81355932 |
|
30.7 |
18.3 |
4.06779661 |
74.44067797 |
|
30.8 |
16 |
4.406779661 |
70.50847458 |
|
30.9 |
14 |
4.745762712 |
66.44067797 |
|
31 |
12 |
5.084745763 |
61.01694915 |
|
31.1 |
10.2 |
5.423728814 |
55.3220339 |
|
31.2 |
8.7 |
5.762711864 |
50.13559322 |
|
31.3 |
7.2 |
6.101694915 |
43.93220339 |
|
31.4 |
5.9 |
6.440677966 |
38 |
|
31.5 |
4.9 |
6.779661017 |
33.22033898 |
|
31.6 |
4 |
7.118644068 |
28.47457627 |
|
31.7 |
3.2 |
7.457627119 |
23.86440678 |
|
31.8 |
2.5 |
7.796610169 |
19.49152542 |
|
31.9 |
2 |
8.13559322 |
16.27118644 |
|
32 |
1.5 |
8.474576271 |
12.71186441 |
|
32.1 |
1.2 |
8.813559322 |
10.57627119 |
|
32.2 |
0.9 |
9.152542373 |
8.237288136 |
|
32.3 |
0.7 |
9.491525424 |
6.644067797 |
|
32.4 |
0.6 |
9.830508475 |
5.898305085 |
|
32.5 |
1.3 |
10.16949153 |
13.22033898 |
|
|
|
|
|
|
|
|
Total
Shares Demanded |
1267.79661 |
There are 1,267 shares demanded at a price of 29.5, too many. So let’s try 29.6
|
Price=29.6 |
|
|
|
|
Intrinsic
Value Estimate |
Number of
Subscribers |
Shares/Person
demanded at given price |
Weighted
Demand |
|
29.5 |
39.8 |
0 |
0 |
|
29.6 |
39.5 |
0 |
0 |
|
29.7 |
38.6 |
0.337837838 |
13.04054054 |
|
29.8 |
37.5 |
0.675675676 |
25.33783784 |
|
29.9 |
36.1 |
1.013513514 |
36.58783784 |
|
30 |
34.2 |
1.351351351 |
46.21621622 |
|
30.1 |
32.3 |
1.689189189 |
54.56081081 |
|
30.2 |
30.1 |
2.027027027 |
61.01351351 |
|
30.3 |
27.8 |
2.364864865 |
65.74324324 |
|
30.4 |
25.4 |
2.702702703 |
68.64864865 |
|
30.5 |
23 |
3.040540541 |
69.93243243 |
|
30.6 |
20.6 |
3.378378378 |
69.59459459 |
|
30.7 |
18.3 |
3.716216216 |
68.00675676 |
|
30.8 |
16 |
4.054054054 |
64.86486486 |
|
30.9 |
14 |
4.391891892 |
61.48648649 |
|
31 |
12 |
4.72972973 |
56.75675676 |
|
31.1 |
10.2 |
5.067567568 |
51.68918919 |
|
31.2 |
8.7 |
5.405405405 |
47.02702703 |
|
31.3 |
7.2 |
5.743243243 |
41.35135135 |
|
31.4 |
5.9 |
6.081081081 |
35.87837838 |
|
31.5 |
4.9 |
6.418918919 |
31.4527027 |
|
31.6 |
4 |
6.756756757 |
27.02702703 |
|
31.7 |
3.2 |
7.094594595 |
22.7027027 |
|
31.8 |
2.5 |
7.432432432 |
18.58108108 |
|
31.9 |
2 |
7.77027027 |
15.54054054 |
|
32 |
1.5 |
8.108108108 |
12.16216216 |
|
32.1 |
1.2 |
8.445945946 |
10.13513514 |
|
32.2 |
0.9 |
8.783783784 |
7.905405405 |
|
32.3 |
0.7 |
9.121621622 |
6.385135135 |
|
32.4 |
0.6 |
9.459459459 |
5.675675676 |
|
32.5 |
1.3 |
9.797297297 |
12.73648649 |
|
|
|
|
|
|
|
|
Total
Shares Demanded |
1108.040541 |
Still too many shares demanded. Let’s try 29.675:
|
Price=29.675 |
|
|
|
|
Intrinsic
Value Estimate |
Number of
Subscribers |
Shares/Person
demanded at given price |
Weighted
Demand |
|
29.5 |
39.8 |
0 |
0 |
|
29.6 |
39.5 |
0 |
0 |
|
29.7 |
38.6 |
0.084245998 |
3.251895535 |
|
29.8 |
37.5 |
0.421229992 |
15.79612468 |
|
29.9 |
36.1 |
0.758213985 |
27.37152485 |
|
30 |
34.2 |
1.095197978 |
37.45577085 |
|
30.1 |
32.3 |
1.432181971 |
46.25947767 |
|
30.2 |
30.1 |
1.769165965 |
53.25189553 |
|
30.3 |
27.8 |
2.106149958 |
58.55096883 |
|
30.4 |
25.4 |
2.443133951 |
62.05560236 |
|
30.5 |
23 |
2.780117944 |
63.94271272 |
|
30.6 |
20.6 |
3.117101938 |
64.21229992 |
|
30.7 |
18.3 |
3.454085931 |
63.20977254 |
|
30.8 |
16 |
3.791069924 |
60.65711879 |
|
30.9 |
14 |
4.128053917 |
57.79275484 |
|
31 |
12 |
4.465037911 |
53.58045493 |
|
31.1 |
10.2 |
4.802021904 |
48.98062342 |
|
31.2 |
8.7 |
5.139005897 |
44.70935131 |
|
31.3 |
7.2 |
5.47598989 |
39.42712721 |
|
31.4 |
5.9 |
5.812973884 |
34.29654591 |
|
31.5 |
4.9 |
6.149957877 |
30.1347936 |
|
31.6 |
4 |
6.48694187 |
25.94776748 |
|
31.7 |
3.2 |
6.823925864 |
21.83656276 |
|
31.8 |
2.5 |
7.160909857 |
17.90227464 |
|
31.9 |
2 |
7.49789385 |
14.9957877 |
|
32 |
1.5 |
7.834877843 |
11.75231676 |
|
32.1 |
1.2 |
8.171861837 |
9.806234204 |
|
32.2 |
0.9 |
8.50884583 |
7.657961247 |
|
32.3 |
0.7 |
8.845829823 |
6.192080876 |
|
32.4 |
0.6 |
9.182813816 |
5.50968829 |
|
32.5 |
1.3 |
9.51979781 |
12.37573715 |
|
|
|
|
|
|
|
|
Total
Shares Demanded |
998.9132266 |
Close enough.
So, this model shows that using the chosen weighting system, the price of a stock with a range of analyst estimates will trade at a higher value than its intrinsic value. In this case, it is 17.5% of one standard deviation. I’m not going to go into deep mathematics to come up with a formula for estimating the premium above intrinsic value where a stock will trade, since it really depends on the weighting on the demand function, and I have no idea what an appropriate weighting might be. Nonetheless, there is some skew here, and it is perhaps important to keep this in mind (perhaps it is not important).
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Historical Results and Commentary