Measuring Single-Asset Risk
Standard deviation is a statistical measure of dispersion around an expected value ( 1999 p. 191). With this, risks can be derived from standard deviation and returns to expected value. It is unlikely that an investor would place his money to single-asset, as such cannot be hedged by diversification, except on specific contracts. In HKSE, 1-month HIBOR future ( 2005) is an example of single-asset usually obtained by a buyer who wants to transfer the risk from interest rate fluctuations. He probably has huge debt from local banks and his interest payments depend largely on interest rates of such banks in which are continuously changing.
To measure the risk position of the buyer, it is necessary to determine individual returns which depends to interest rate-sensitive indicators, say, Hong Kong’s levels of FDI and the probability of their occurrence. Let us assumed that the buyer after thorough research has classified high, medium and low FDI levels with probabilities of occurrence of 25%, 50% and 25% respectively and probable returns at 15%, 12% and 8% respectively. After calculating the expected value of a return, risk measurement can be conducted by deriving it from standard deviation (see computation 1).
The computation shows that the expected value of the buyer’s return is 11.75% and his risk is 2.49%. Statistically, using the normal probability distribution (see figure 1), it can said that there is 68% chance that the actual return will lie within ±1σ of 11.75% (the mean) and 95% chance within ±2σ of 11.75%. However, determining the risk of the venture has yet to be completely derived. The normal distribution merely mimic the rule of return-risk trade-offs. In ±1σ scenario, there is smaller dispersion (risk) coupled with smaller upper limit of 14.24% but minimal lower limit of 9.26%. In contrast, the ±2σ scenario shows that there is higher dispersion (risk) coupled with larger upper limit of 16.73% but too low lower limit of 6.77%. Question of investment alternatives become useful to this finding to obtain comparative statistics. At this moment, the investor can simply assess his attitude to risk with reference to vital factors, say, his liquidity.
Measuring Portfolio Risk
Extending the analysis of the cautionary finding in the preceding example, we can derive the risk position of the buyer with more accuracy when we will also compute for another type of asset alternative (say, the 3-month HIBOR futures). Assuming that the buyer opted to have follow-up research for this and come-up with information in Table 1, which for the purpose of comparison, situated beside the 1-month HIBOR futures. It can be observed that 3-month HIBOR future ( 2005) is more sensitive since it can be classified narrowly to very high FDI, high FDI, moderately high FDI, and so on. This, possibly, is caused by higher risk (and return) attached with longer exposure to market and economy fluctuations.
In computing for the expected value and standard deviation of the 3-month HIBOR (see computation 2), it is still contestable what is the optimal investment destination. This can be answered by coefficient of variation (see computation 3). Thus, the 3-month HIBOR future is computed not only the less risky investment option but more profitable than the 1-month HIRBOR computed earlier. Someone would ask, where did the expected value of return will come from noting that the purpose of such purchase is for the buyer to offset substantial fluctuations of banks’ interests rates where he has outstanding loans and interest payments? This can be resolved for the fact that those HIBORs are also tradable where a large amount in a transaction would not only shield the buyer from interest rate shocks but also derive profits (losses) from them.
Four Ways of Common Stock Valuation
Zero and Constant Dividend Growth
Expectations on future dividend payments primarily characterize the value of ordinary (common) shares. This is an assumption that the firm will not be sold or take-over to/by another firm (p. 260). Figure 2 shows the basic formula to determine common stock value. However, since firm performance and consequently its dividend payments can only be estimated, placing a numerical value in the formula may lead shareholders to exaggeration or even underestimation. Due to this, there are two specific assumptions for guidance; namely, zero dividend growth and constant dividend growth (p. 261).
For example, assuming that an HKSE listed firm Esprit is expected to pay a dividend of HK.50 indefinitely and the required rate of return is 12%. As observed, the expected dividend is termed as ‘indefinitely’ to acknowledge that no growth will ensue in the meantime probably such is applicable to some countries in the European market of Esprit due to stiff competition ( 2006). By canceling the period of varying dividend growth, the figure 2 formula would simply derive the answer from the quotient of expected dividend per share and required rate of return equivalent to HK.17. On the other hand, assuming that the new woman’s apparel of the firm has enticed the North American market that resulted to expected constant dividend growth of 5% per year. Using figure 2, the answer is HK$ 7.50.
As observed, the positive reaction of North American market indirectly increased the stock value primarily due to higher expected future cash flows. However, such assumptions should not be easily taken by shareholders since the crucial part of the computation lies in accurate finding of the required rate of return and dividend growth. The former will be tackled in the later discussion about cost of capital while the latter can be derived using the next discussion about growth dividend estimation.
Estimating the Growth Rate of Dividend
For example, an investor is confronted with Esprit financial information as follows:
Appendices
Computation 1
E(r)=r1 P(r1 )+r2 P(r2 )+…+rn P(rn )
where,
ri
=
rate of return for the identified ith outcome
P(ri)
=
probability of earning return i for the identified outcome
n
=
number of possible outcomes
So,
E(r) = 0.25(15%)+0.50(12%)+0.25(8%) = 11.75%
where
Var(r )
=
the variance of returns
σr
=
the standard deviation of returns
r̄
=
the expected or mean value of a return
ri
=
return for the ith outcome
P(ri )
=
probability of occurrence of the ith outcome
n
=
number of outcomes considered
(2)−(3)
(4)×(4)
(5)×(6)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
I
ri
r̄
ri−r̄
(ri−r̄)2
P(ri)
(ri−r̄)2×P(ri)
1
15%
11.75%
3.25%
10.56%
0.25
2.64%
2
12
11.75
0.25
0.06
0.50
0.03
3
8
11.75
−3.75
14.06
0.25
3.52
Finally, our standard deviation is 2.49%.
Computation 2
Rate of Return
Probability of Occurrence
Expected Value
6
0.05
12
-6
36
1.8
8
0.1
-4
16
1.6
10
0.2
-2
4
0.8
12
0.3
0
0
0
14
0.2
2
4
0.8
16
0.1
4
16
1.6
18
0.05
6
36
1.8
8.4
2.89%
1-month
3-month
Expected value
11.75%
12
Std deviation
2.49%
2.89%
Computation 3
1-month
3-month
Expected value
11.75%
12
Std deviation
2.49%
2.89%
Coefficient of Variation
0.211915
0.002408
Computation 4
Computation High-Decline-Stable (Motley Fool.com)
Next, we value the stable growth period:
DPS = .00 (1.06) = .12
Ks = 12.8%
g = 6%
.12 / (.128-0.06) = .18
Next, we must calculate the present value of the dividends.
.18 / (1.1239)5 = .39
When calculating the present value of the dividends of the stable growth period, we use the same required rate of return as the high-growth phase and raise it to the fifth power for a five-year example like the one above.
Adding the two values, we get: .39 + .94 = .33
Figure 1
Figure 2
Formula of basic equity valuation model
The basic equity share valuation model is given by: 4
where,
SV0
=
value (price) of the share at time zero
Dt
=
expected dividend per share (DPS) at end of year t (t=1, 2, …, n, …, ∞)
r
=
required annual rate of return on the share/discount rate
∞
=
symbol denoting infinity
Zero Growth
Constant Growth
Figure 3
E(ri )=Rf +βi (ERm −Rf )
where,
E(ri )
=
required return on asset/share i
Rf
=
risk-free rate of return
βi
=
beta coefficient for asset/share i
ERm
=
expected market return, that is the return expected on the market portfolio of shares
Table 1
Asset A
Asset B
Rate of return (%)
Probability of occurrence, P(ri)
Rate of return (%)
Probability of occurrence, P(ri)
6
0.05
8
0.25
8
0.10
10
0.50
10
0.20
12
0.25
12
0.30
14
0.20
16
0.10
18
0.05
Table 2: Future value interest factor (FVIF) for £1 compounded at r per cent for n periods (p. 695)
n
11%
12%
13%
14%
15%
16%
17%
18%
19%
20%
1
1.110
1.120
1.130
1.140
1.150
1.160
1.170
1.180
1.190
1.200
2
1.232
1.254
1.277
1.300
1.322
1.346
1.369
1.392
1.416
1.440
3
1.368
1.405
1.443
1.482
1.521
1.561
1.602
1.643
1.685
1.728
4
1.518
1.574
1.630
1.689
1.749
1.811
1.874
1.939
2.005
2.074
5
1.685
1.762
1.842
1.925
2.011
2.100
2.192
2.288
2.386
2.488
6
1.870
1.974
2.082
2.195
2.313
2.436
2.565
2.700
2.840
2.986
7
2.076
2.211
2.353
2.502
2.660
2.826
3.001
3.185
3.379
3.583
8
2.305
2.476
2.658
2.853
3.059
3.278
3.511
3.759
4.021
4.300
9
2.558
2.773
3.004
3.252
3.518
3.803
4.108
4.435
4.785
5.160
10
2.839
3.106
3.395
3.707
4.046
4.411
4.807
5.234
5.695
6.192
11
3.152
3.479
3.836
4.226
4.652
5.117
5.624
6.176
6.777
7.430
12
3.498
3.896
4.334
4.818
5.350
5.936
6.580
7.288
8.064
8.916
13
3.883
4.363
4.898
5.492
6.153
6.886
7.699
8.599
9.596
10.699
14
4.310
4.887
5.535
6.261
7.076
7.987
9.007
10.147
11.420
12.839
15
4.785
5.474
6.254
7.138
8.137
9.265
10.539
11.974
13.589
15.407
16
5.311
6.130
7.067
8.137
9.358
10.748
12.330
14.129
16.171
18.488
17
5.895
6.866
7.986
9.276
10.761
12.468
14.426
16.672
19.244
22.186
18
6.543
7.690
9.024
10.575
12.375
14.462
16.879
19.673
22.900
26.623
19
7.263
8.613
10.197
12.055
14.232
16.776
19.748
23.214
27.251
31.948
20
8.062
9.646
11.523
13.743
16.366
19.461
23.105
27.393
32.429
38.337
21
8.949
10.804
13.021
15.667
18.821
22.574
27.033
32.323
38.591
46.005
22
9.933
12.100
14.713
17.861
21.644
26.186
31.629
38.141
45.923
55.205
23
11.026
13.552
16.626
20.361
24.891
30.376
37.005
45.007
54.648
66.247
24
12.239
15.178
18.788
23.212
28.625
35.236
43.296
53.108
65.031
79.496
25
13.585
17.000
21.230
26.461
32.918
40.874
50.656
62.667
77.387
95.395
30
22.892
29.960
39.115
50.949
66.210
85.849
111.061
143.367
184.672
237.373
40
64.999
93.049
132.776
188.876
267.856
378.715
533.846
750.353
1051.642
1469.740
50
184.559
288.996
450.711
700.197
1083.619
1670.669
2566.080
3927.189
5988.730
9100.191
Credit:ivythesis.typepad.com
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