Beta estimation and the cost of equity
for listed shipping companies
Wolfgang Drobetz, Christina Menzel, and Henning Schröder
Baltic Exchange Shipping Risk Management Symposium| Hamburg | October 2014
Beta estimation and the cost of equity for listed shipping companies
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Discount rates

Discount rates are a critical ingredient in discounted cash flow valuation (the NPV
formula). Errors in estimating the discount rate (i.e., the opportunity cost of capital for investors) or mismatching cash flows and discount rates can lead to serious
errors in valuation.

The discount rate used must be consistent with both the riskiness and the type of
cash flows being discounted.

Equity vs. firm: If the cash flows being discounted are cash flows to equity, the appropriate discount rate is the cost of equity. The cost of equity is the rate of return that investors
require to make an equity investment in a firm. If the cash flows are the cash flows to the
firm, the appropriate discount rate is the cost of capital.

Currency: The currency in which the cash flows are estimated should also be the currency
in which the discount rate is estimated.

Nominal vs. real: If the cash flows being discounted are nominal cash flows (i.e., reflect
expected inflation), the discount rate should also be nominal.
October 2014
Baltic Exchange Symposium
Hamburg
Beta estimation and the cost of equity for listed shipping companies
|2
Cost of equity
The cost of equity is higher for riskier investments and lower for safer investments


Assumption: Investors like overall portfolio reward (expected return) and dislike overall
portfolio risk (variance or standard deviation of return).

Most risk and return models in finance assume that investors are well diversified,
thus the only risk an investor perceives in an investment is the risk that cannot be
diversified away (i.e., market or non-diversifiable risk).

The risk that should be rewarded (and built into the equity discount rate) in valuation should be the risk perceived by the marginal investor in the investment.

The contribution to overall portfolio risk is the market beta of a project – a measure of the
project’s “toxicity”.

A project that decreases in value when the market decreases in value, and increases when
the market increases, has a positive beta – it is toxic, and investors do not like it.

A project with a low beta helps an investor who holds the market portfolio to reduce the
overall investment risk.
October 2014
Baltic Exchange Symposium
Hamburg
Beta estimation and the cost of equity for listed shipping companies
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Cost of equity: The Capital Asset Pricing Model (CAPM)
The CAPM is a model that provides an appropriate expected rate of return (or cost
of equity) for each project.


An investment’s cost of equity is lower when it offers diversification benefits for an investor who holds the market portfolio, i.e., less required reward for less risk contribution.
The market beta is the model’s measure of risk contribution.


The CAPM posits that investors care only about project market betas, because these measure the risk components which investors holding the (perfectly diversified) market portfolio cannot diversify away.

Projects contributing more risk (higher market beta) require a higher expected rate of return for investors to want them; projects contributing less risk (lower market beta) require
a lower expected rate of return.
Cost of equity ≡ Expected return = Risk-free rate + [Beta×Market risk premium]
𝐸 𝑅 = 𝑅𝑓 + 𝛽 × 𝐸 𝑅𝑚 − 𝑅𝑓
October 2014
Baltic Exchange Symposium
Hamburg
Beta estimation and the cost of equity for listed shipping companies
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Estimating the CAPM inputs (1)
Cost of equity ≡ Expected return = Risk-free rate + [Beta×Market risk premium]
𝐸 𝑅 = 𝑅𝑓 + 𝛽 × 𝐸 𝑅𝑚 − 𝑅𝑓
For an investment to be risk-free, it has to have…


No default risk

No reinvestment risk
Therefore, the risk-free rate in valuation depends on when the cash flows are expected to occur (term structure) and will vary across time.



For valuation puroses, the time horizon is generally long, thus a long-term (or duration
matched) risk-free rate is preferable to a short-term rate (if the investor has to pick one).
The market risk premium is not revealed in market prices, thus most investors use
historical premiums (i.e., the premium that stocks have historically earned over
riskless securities).
October 2014
Baltic Exchange Symposium
Hamburg
Beta estimation and the cost of equity for listed shipping companies
|5
Estimating the CAPM inputs (2)
Source: Credit Suisse Global Investment Returns Yearbook 2013
October 2014
Baltic Exchange Symposium
Hamburg
Beta estimation and the cost of equity for listed shipping companies
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Estimating the CAPM inputs (3)
Note: Geometric averages
Source: Credit Suisse
Global Investment Returns
Yearbook 2013
October 2014
Baltic Exchange Symposium
Hamburg
Beta estimation and the cost of equity for listed shipping companies
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Estimating the CAPM inputs (4)
Historical averages: a few caveats…


Length of sample period?

Long-term vs. short-term bonds?

Geometric vs. arithmetic rates of return?

Statistical significance? (margin of error)

Peso problems? (tiny probability of desasters that just happened not to happen; survivorship bias and “good luck”)

High historical returns may indicate low future expected rates of return (mean reversion)
Beta estimation:


Regress excess stock returns against excess return:
with
 The slope of the market model regression corresponds to the beta of the stock, and measures the riskiness of the stock.
October 2014
Baltic Exchange Symposium
Hamburg
Beta estimation and the cost of equity for listed shipping companies
|8
Estimating the CAPM inputs (5)
Beta estimation: a few caveats…


Length of the estimation period

Return interval and market index

Accuracy of estimate (margin of error may require beta shrinking towards 1)
0.6
Market model regression: An example
Daiichi Chuo Kisen Kaisha: y = (‒0,0025) + 1,0259•x
Monthly company
excess return
0.4
0.2
0
-0.3
-0.2
-0.1
 ≡ slope of line
0
-0.2
0.1
0.2
Monthly MSCI World
excess return
-0.4
October 2014
Baltic Exchange Symposium
Hamburg
Beta estimation and the cost of equity for listed shipping companies
|9
Determinants of betas
Beta of equity
Beta of firm (asset beta)
Nature of product or service
offered:
Operating Leverage:
Other things equal, the more
discretionary the product or
service, the higher the beta.
Other things equal, the greater
the ratio of fixed costs to total
costs, the higher the beta of
the company.
Implications:
Implications:



Cyclical firms have higher
betas
Luxury and high priced
goods/service firms have
higher betas
Growth firms have higher
betas
October 2014


Financial Leverage:
Other things equal, the greater
the proportion of capital that a
firm raises from debt, the
higher the equity beta.
Implication:

Highly levered firms should
have higher betas
Firms with high infrastructure needs and rigid
cost structures have higher
betas
Smaller and younger firms
have higher betas
Source: Damodaran, 2012
Baltic Exchange Symposium
Hamburg
Beta estimation and the cost of equity for listed shipping companies
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Different approaches to estimate betas of shipping companies
Shipping companies are prone to have high betas…


…highly cyclical, high operating leverage, and high financial leverage
Earlier empirical studies report low betas using the market model regression


Prior studies use small and old samples, but market betas may have increased over time

Market betas may be time-varying depending on the economic conditions
We use static and dynamic beta estimation methods…


Standard market model regression

Fama-French three-factor model (controlling for size and value premia)

Scholes-Williams method and Dimson’s AC method (controlling for infrequent trading)

Rolling window regression approach (rolling window of 60 months)

Kalman filter approach (conditional coefficient estimates by recursively estimating dynamic betas from the market model)

Bivariate M-GARCH approach (conditional variances and covariances)
October 2014
Baltic Exchange Symposium
Hamburg
Beta estimation and the cost of equity for listed shipping companies
| 11
Data description (1)
October 2014
Baltic Exchange Symposium
Hamburg
Beta estimation and the cost of equity for listed shipping companies
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Data description (2)
Benchmark for market model regression: MSCI World Market (TR)
October 2014
Baltic Exchange Symposium
Hamburg
Beta estimation and the cost of equity for listed shipping companies
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Static beta estimates
October 2014
Baltic Exchange Symposium
Hamburg
Beta estimation and the cost of equity for listed shipping companies
| 14
Dynamic beta estimates
October 2014
Baltic Exchange Symposium
Hamburg
Beta estimation and the cost of equity for listed shipping companies
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Beta estimates over sample period: Daiichi Chuo Kisen Kaisha
3
2.5
2
1.5
1
0.5
0
1996
1998
Kalman Filter
October 2014
2000
Rolling Window
2002
2004
M-GARCH
2006
Fama-French
Baltic Exchange Symposium
2008
CAPM
2010
Dimson
2012
Scholes-Williams
Hamburg
Beta estimation and the cost of equity for listed shipping companies
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Dynamic beta estimates over sample period
October 2014
Baltic Exchange Symposium
Hamburg
Beta estimation and the cost of equity for listed shipping companies
| 17
Determinants of beta
October 2014
Baltic Exchange Symposium
Hamburg
Beta estimation and the cost of equity for listed shipping companies
Estimated cost of capital
October 2014
| 18
Assumptions:
• Risk-free rate: 2.5% (based on U.S. T-bond yield)
• World USD equity risk premium: 4.1%
• Beta estimation based on Kalman filter
Baltic Exchange Symposium
Hamburg